d his (FILE 'HOME' ENTERED AT 10:08:33 ON 03 APR 1997) FILE 'INSPEC' ENTERED AT 10:09:18 ON 03 APR 1997 ACT MROWKA/A --------- L1 ( 1053)SEA FILE=INSPEC (RELAXATION METHOD?/TI,CT,ST) L2 ( 2)SEA FILE=INSPEC L1 AND REVIEW/TI,CT L3 ( 2)SEA FILE=INSPEC L1 AND REVIEW/ST L4 ( 4)SEA FILE=INSPEC L2 OR L3 L5 ( 12788)SEA FILE=INSPEC A4710/CC L6 ( 31)SEA FILE=INSPEC L1 AND L5 L7 ( 382)SEA FILE=INSPEC (RELAXATION METHOD?/TI) L8 404 SEA FILE=INSPEC L4 OR L6 OR L7 --------- => d bib ab 1-4,6,7,10,11,13,14-17,19-21,24,27,29,32,33,37,41,44-47,50,51,58,66,69,71,78,88,96,99,101,125,126,136,137,145,155 L8 ANSWER 1 OF 404 INSPEC COPYRIGHT 1997 IEE AN 97:5515417 INSPEC DN A9708-4755E-001 TI An implicit ***relaxation*** ***method*** for calculating steady two-dimensional flows of a spontaneously condensing vapour. AU Kosolapov, Yu.S.; Liberzon, A.S. SO Computational Mathematics and Mathematical Physics (1996) vol.36, no.6, p.805-15. 23 refs. Doc. No.: S0965-5425(96)00098-1 Published by: Elsevier Price: CCCC 0965-5425/96/$24.00+.00 CODEN: CMMPA9 ISSN: 0965-5425 SICI (Trl): 0965-5425(1996)36:6L.805:IRMC;1-7 Translation of: Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki (1996) vol.36, no.6, p.138-51. 23 refs. CODEN: ZVMFAN ISSN: 0044-4669 SICI: 0044-4669(1996)36:6L.138;1-7 DT Journal; Translation Abstracted TC Theoretical CY Russian Federation; United Kingdom LA English AB An implicit monotone relaxation method of second-order of accuracy with respect to the space coordinates for calculating steady two-dimensional flows of spontaneously condensing and wet steam is constructed. Possible applications of the method are demonstrated using the examples of the calculation of flows of spontaneously condensing vapour in nozzles and turbine cascades. A comparison is made with calculation and the experimental results obtained elsewhere. L8 ANSWER 2 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5495029 INSPEC DN B9703-0290F-025; C9703-4130-037 TI Convergence of waveform ***relaxation*** ***methods*** for differential-algebraic systems. AU Jackiewicz, Z. (Dept. of Math., Arizona State Univ., Tempe, AZ, USA); Kwapisz, M. SO SIAM Journal on Numerical Analysis (Dec. 1996) vol.33, no.6, p.2303-17. 25 refs. Published by: SIAM Price: CCCC 0036-1429/96/$2.00+0.15 CODEN: SJNAEQ ISSN: 0036-1429 SICI: 0036-1429(199612)33:6L.2303:CWRM;1-1 DT Journal TC Theoretical CY United States LA English AB This paper gives sufficient conditions for existence and uniqueness of solutions and for the convergence of Picard iterations and more general waveform relaxation methods for differential-algebraic systems of neutral type. The results are obtained by the contraction mapping principle on Banach spaces with weighted norms and by the use of the Perron-Frobenius theory of nonnegative and nonreducible matrices. It is demonstrated that waveform relaxation methods are convergent faster than the classical Picard iterations. L8 ANSWER 3 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5468386 INSPEC DN B9702-0290P-020; C9702-4170-023 TI Fourier-Laplace analysis of the multigrid waveform ***relaxation*** ***method*** for hyperbolic equations. AU Shlomo Ta'Asan (Dept. of Math., Carnegie Mellon Univ., Pittsburgh, PA, USA); Hong Zhang SO BIT (Dec. 1996) vol.36, no.4, p.831-41. 19 refs. Published by: BIT Found CODEN: BITTEL ISSN: 0006-3835 SICI: 0006-3835(199612)36:4L.831:FLAM;1-7 DT Journal TC Theoretical CY Denmark LA English AB The multigrid waveform relaxation (WR) algorithm has been fairly studied and implemented for parabolic equations. It has been found that the performance of the multigrid WR method for a parabolic equation is practically the same as that of multigrid iteration for the associated steady state elliptic equation. However, the properties of the multigrid WR method for hyperbolic problems are relatively unknown. This paper studies the multigrid acceleration to the WR iteration for hyperbolic problems, with a focus on the convergence comparison between the multigrid WR iteration and the multigrid iteration for the corresponding steady state equations. Using a Fourier-Laplace analysis in two case studies, it is found that the multigrid performance on hyperbolic problems no longer shares the close resemblance in convergence factors between the WR iteration for parabolic equations and the iteration for the associated steady state equations. L8 ANSWER 4 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5467447 INSPEC DN A9704-8710-001; C9702-1290L-110 TI Fast multiple alignment of ungapped DNA sequences using information theory and a ***relaxation*** ***method*** . AU Schneider, T.D. (Lab. of Math. Biol., Nat. Cancer Inst., Frederick, MD, USA); Mastronarde, D.N. SO Discrete Applied Mathematics (5 Dec. 1996) vol.71, no.1-3, p.259-68. 22 refs. Published by: Elsevier Price: CCCC 0166-218X/96/$15.00 CODEN: DAMADU ISSN: 0166-218X SICI: 0166-218X(19961205)71:1/3L.259:FMAU;1-3 DT Journal TC Theoretical CY Netherlands LA English AB An information theory based multiple alignment ("Malign") method was used to align the DNA binding sequences of the OxyR and Fis proteins, whose sequence conservation is so spread out that it is difficult to identify the sites. In the algorithm described, the information content of the sequences is used as a unique global criterion for the quality of the alignment. The algorithm uses look-up tables to avoid recalculating computationally expensive functions such as the logarithm. Because there are no arbitrary constants and because the results are reported in absolute units (bits), the best alignment can be chosen without ambiguity. Starting from randomly selected alignments, a hill-climbing algorithm can track through the immense space of sn combinations, where s is the number of sequences and n is the number of positions possible for each sequence. Instead of producing a single alignment, the algorithm is fast enough that one can afford to use many start points and to classify the solutions. Good convergence is indicated by the presence of a single well-populated solution class having higher information content than other classes. The existence of several distinct classes for the Fis protein indicates that those binding sites have self-similar features. L8 ANSWER 6 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5462446 INSPEC DN A9703-0720F-002 TI Calorimeter apparatus using a thermal ***relaxation*** ***method*** . AU Azechi, L.S.; da Costa, R.F.; Medina, A.N.; Gandra, F.C.G. (Dept. de Eletronica Quantica, UNICAMP, Campinas, Brazil) SO Revista de Fisica Aplicada e Instrumentacao (June 1995) vol.10, no.2, p.70-5. 8 refs. Published by: Sociedade Brasileira Fisica CODEN: RFAIEE ISSN: 0102-6895 SICI: 0102-6895(199506)10:2L.70:CAUT;1-6 DT Journal TC Experimental CY Brazil LA Portuguese AB In this work a specific heat apparatus based on the sample thermal relaxation method is presented. The system is designed for small samples and can be implemented for any temperature range. A full description of the system is given together with some results which ensure the capability of the method. L8 ANSWER 7 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5443790 INSPEC DN B9701-6140C-449; C9701-1250-249 TI Robust ***relaxation*** ***method*** for structural matching under uncertainty. AU Horiuchi, T. (Inst. of Inf. Sci. & Electron., Tsukuba Univ., Ibaraki, Japan); Yamamoto, K.; Yamada, H. SO Proceedings of the 13th International Conference on Pattern Recognition Los Alamitos, CA, USA: IEEE Comput. Soc. Press, 1996. p.176-80 vol.2 of 4 vol. (xxxi+976+xxix+922+xxxi+1008+xxix+788) pp. 8 refs. Conference: Vienna, Austria, 25-29 Aug 1996 Sponsor(s): Int. Assoc. Pattern Recognition Price: CCCC 1015-4851/96/$5.00 ISBN: 0-8186-7282-X DT Conference Article TC Theoretical CY United States LA English AB Probabilistic relaxation labeling processes have been widely used in many different fields including image processing, pattern recognition, and artificial intelligence. However it is impossible to express conviction degrees to be related to human subjectivity. We propose a novel relaxation scheme called "robust relaxation" for structural matching under uncertainty. Since this method is constructed on the Dempster-Shafer measure, the above problem can be solved. L8 ANSWER 10 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5411436 INSPEC DN B9612-0250-021; C9612-1160-031 TI An epsilon - ***relaxation*** ***method*** for generalized separable convex cost network flow problems. AU Tseng, P. (Dept. of Math., Washington Univ., Seattle, WA, USA); Bertsekas, D.P. SO Integer Programming and Combinatorial Optimization. 5th International IPCO Conference Proceedings Editor(s): Cunningham, W.C.; McCormick, S.T.; Queyranne, M. Berlin, Germany: Springer-Verlag, 1996. p.85-93 of x+504 pp. 21 refs. Conference: Vancouver, BC, Canada, 3-5 June 1996 Sponsor(s): Math. Programming Soc ISBN: 3-540-61310-2 DT Conference Article TC Theoretical CY Germany, Federal Republic of LA English AB Proposes an extension of the epsilon -relaxation method to generalized network flow problems with separable convex cost. The method maintains epsilon -complementary slackness satisfied at all iterations and adjusts the arc flows and the node prices so as to satisfy flow conservation upon termination. Each iteration of the method involves either a price change at a node or a flow change at an arc or a flow change around a simple cycle. Complexity bounds for the method are derived. For one implementation employing epsilon -scaling, the bound is polynomial in the number of nodes N, the number of arcs A, a certain constant Gamma depending on the arc gains, and ln( epsilon 0/ epsilon ), where epsilon 0 and epsilon denote, respectively, the initial and the final epsilon . L8 ANSWER 11 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5400764 INSPEC DN C9612-4130-004 TI A class of parallel nonlinear multisplitting ***relaxation*** ***methods*** for the large sparse nonlinear complementarity problems. AU Zhong-Zhi Bai (Acad. Sinica, Beijing, China); De-Ren Wang SO Computers & Mathematics with Applications (Oct. 1996) vol.32, no.8, p.79-95. 15 refs. Doc. No.: S0898-1221(96)00169-1 Published by: Elsevier Price: CCCC 0898-1221/96/$15.00+0.00 CODEN: CMAPDK ISSN: 0898-1221 SICI: 0898-1221(199610)32:8L.79:CPNM;1-7 DT Journal TC Theoretical CY United Kingdom LA English AB By making use of the nonlinear multisplitting and nonlinear relaxation techniques, we present a class of parallel nonlinear multisplitting successive overrelaxation methods for solving large sparse nonlinear complementarity problems on modern high-speed multiprocessors. These new methods particularly include the so-called nonlinear multisplitting SOR-Newton method, the nonlinear multisplitting SOR-chord method, and the nonlinear multisplitting SOR-Steffensen method. Under suitable conditions, we establish local convergence theories of the new methods, and investigate their asymptotic convergence rates. Numerical results show that our new methods are feasible and efficient for parallel solution of nonlinear complementarity problems. L8 ANSWER 13 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5350970 INSPEC DN B9610-6140C-043; C9610-5260B-035 TI Feature detection of moving images using a hierarchical ***relaxation*** ***method*** . AU Dingding Chang; Hashimoto, S. (Dept. of Appl. Phys., Waseda Univ., Tokyo, Japan) SO IEICE Transactions on Information and Systems (July 1996) vol.E79-D, no.7, p.997-9. 14 refs. Published by: Inst. Electron. Inf. & Commun. Eng CODEN: ITISEF ISSN: 0916-8532 SICI: 0916-8532(199607)E79D:7L.997:FDMI;1-D DT Journal TC Practical CY Japan LA English AB A hierarchical relaxation method is presented for detecting local features in moving images. The relaxation processes are performed on the temporal spatial pyramid, which is a multi resolution data structure for the moving images. The accurate and high speed edge detection can be obtained by using information in the neighboring frames as well as the processed results in the higher layers of the pyramid. L8 ANSWER 14 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5342789 INSPEC DN B9609-0290P-006; C9609-4170-007 TI Chaotic waveform ***relaxation*** ***methods*** for dynamical systems. AU Yongzhong Song (Dept. of Math., Nanjing Normal Univ., China) SO Applied Mathematics and Computation (Aug. 1996) vol.78, no.1, p.83-100. 9 refs. Published by: Elsevier Price: CCCC 0096-3003/96/$15.00 CODEN: AMHCBQ ISSN: 0096-3003 SICI: 0096-3003(199608)78:1L.83:CWRM;1-9 DT Journal TC Theoretical CY United States LA English AB For solving the large dynamical systems of initial value problems that can be described by a system of mixed implicit differential equations, the waveform relaxation (WR) methods are proposed and investigated by some mathematicians. In this paper, in order to compute the WR methods on parallel processors and to avoid the synchronization costs, the chaotic waveform relaxation (WR) methods are presented and their convergence is investigated. As for the special cases, the nonlinear ODEs, linear ODEs and semi-explicit DAEs are discussed, respectively. L8 ANSWER 15 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5342518 INSPEC DN A9618-4710-014; C9609-7320-087 TI Data-parallel lower-upper ***relaxation*** ***method*** for the Navier-Stokes equations. AU Wright, M.J.; Candler, G.V.; Prampolini, M. (Minnesota Univ., Minneapolis, MN, USA) SO AIAA Journal (July 1996) vol.34, no.7, p.1371-7. 15 refs. Published by: AIAA Price: CCCC 0001-1452/96/$2.00+.50 CODEN: AIAJAH ISSN: 0001-1452 SICI: 0001-1452(199607)34:7L.1371:DPLU;1-2 DT Journal TC Theoretical CY United States LA English AB The lower-upper symmetric Gauss-Seidel method is modified for the simulation of viscous flows on massively parallel computers. The resulting diagonal data-parallel lower-upper relaxation (DP-LUR) method is shown to have good convergence properties on many problems. However, the convergence rate decreases on the high cell aspect ratio grids required to simulate high Reynolds number flows. Therefore, the diagonal approximation is relaxed, and a full matrix version of the DP-LUR method is derived. The full matrix method retains the data-parallel properties of the original and reduces the sensitivity of the convergence rate to the aspect ratio of the computational grid. Both methods are implemented on the Thinking Machines CM-5, and a large fraction of the peak theoretical performance of the machine is obtained. The low memory use and high parallel efficiency of the methods make them attractive for large-scale simulation of viscous flows. L8 ANSWER 16 OF 404 INSPEC COPYRIGHT 1997 FIZ KARLSRUHE AN 96:5323906 INSPEC DN A9616-4740K-008 TI ***Relaxation*** ***method*** for 3-D problems in supersonic aerodynamics. AU Karamyshev, V.; Kovenya, V.; Cherny, S. (Inst. of Comput. Technol., Rossijskaya Akad. Nauk, Novosibirsk, Russia) SO Fourteenth International Conference on Numerical Methods in Fluid Dynamics. Proceedings of the Conference Editor(s): Deshpande, S.M.; Desai, S.S.; Narasimha, R. Berlin, Germany: Springer-Verlag, 1995. p.280-4 of xiii+588 pp. 3 refs. Conference: Bangalore, India, 11-15 July 1994 ISBN: 3-540-59280-6 DT Conference Article TC Theoretical CY Germany, Federal Republic of LA English AB A version of global iterations method is considered for the numerical solution of stationary 3-D problems of supersonic aerodynamics with the accelerated convergence of internal iteration processes in marching cross-sections by the least square method. L8 ANSWER 17 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5311610 INSPEC DN B9608-0290Z-005; C9608-4190-003 TI The monotone convergence of a class of parallel nonlinear ***relaxation*** ***methods*** for nonlinear complementarity problems. AU Zhong-Zhi Bai (State Key Lab., Acad. Sinica, Beijing, China) SO Computers & Mathematics with Applications (June 1996) vol.31, no.12, p.17-33. 26 refs. Doc. No.: S0898-1221(96)00073-9 Published by: Elsevier Price: CCCC 0898-1221/96/$15.00+0.00 CODEN: CMAPDK ISSN: 0898-1221 SICI: 0898-1221(199606)31:12L.17:MCCP;1-9 DT Journal TC Practical; Theoretical CY United Kingdom LA English AB We set up a class of parallel nonlinear multisplitting AOR methods by directly multisplitting the nonlinear mapping involved in the nonlinear complementarity problems. The different choices of the relaxation parameters can yield all the known and a lot of new relaxation methods, as well as a lot of new relaxed parallel nonlinear multisplitting methods for solving the nonlinear complementarity problems. The two-sided approximation properties and the influences on the convergence rates from the relaxation parameters about our new methods are shown, and sufficient conditions guaranteeing the methods to converge globally are discussed. Finally, a lot of numerical results show that our new methods are feasible and efficient. L8 ANSWER 19 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5280714 INSPEC DN C9607-1250-142 TI A ***relaxation*** ***method*** to classification of straight line segments. AU Faber, P. (Dept. of Math. & Inf. Sci., Friedrich-Schiller-Univ., Jena, Germany) SO Proceedings of The First International Conference on Visual Information Systems Melbourne, Vic., Australia: Victoria Univ. Technol, 1996. p.283-92 of viii+585 pp. 16 refs. Conference: Melbourne, Vic., Australia, 5-6 Feb 1996 DT Conference Article TC New Development; Practical CY Australia LA English AB A new approach for classifying characteristic edge segments is presented. The algorithm is based on a relaxation method. It uses local features of edge segments for initialization and global relations between all edge segments to update the values of interpretation. Several updating operators F are investigated with respect to their characteristics, of which the correctness of the results and the iteration steps (speed of convergence) are most important. Some experimental results on intensity images are given in this paper to highlight the distinctive features of the presented technique. L8 ANSWER 20 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5269829 INSPEC DN C9607-1290-001 TI Incorporating facet-inducing inequalities into graphical-construct- based Lagrangian ***relaxation*** ***methodologies*** . AU Ali, A.I.; Shmerling, S. (Sch. of Manage., Massachusetts Univ., Amherst, MA, USA) SO Operations Research Letters (Feb. 1996) vol.18, no.4, p.177-84. 32 refs. Published by: Elsevier Price: CCCC 0167-6377/96/$15.00 CODEN: ORLED5 ISSN: 0167-6377 SICI: 0167-6377(199602)18:4L.177:IFII;1-W DT Journal TC Practical; Theoretical CY Netherlands LA English AB This paper shows that facet-inducing inequalities can be incorporated into graphical-construct-based Lagrangian relaxation methodologies by including them as dualized constraints. It develops an algorithm that successively identifies additional facet-inducing inequalities and incorporates them into the Lagrangian function. Computational experience shows that the algorithm can resolve duality gaps using relatively few facet-inducing inequalities. L8 ANSWER 21 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5268027 INSPEC DN B9606-8110B-084; C9606-3340H-169 TI Practical approach to unit commitment problem using genetic algorithm and Lagrangian ***relaxation*** ***method*** . AU Ohta, T.; Matsui, T.; Takata, T. (Chubu Electric Power Co. Inc., Nagoya, Japan); Kato, M.; Aoyagi, M.; Kunugi, M.; Shimada, K.; Nagata, J. SO ISAP '96. International Conference on Intelligent Systems Applications to Power Systems Proceedings (Cat. No.96TH8152) Editor(s): Mohammed, O.A.; Tomsovic, K. New York, NY, USA: IEEE, 1996. p.434-40 of xxv+476 pp. 7 refs. Conference: Orlando, FL, USA, 28 Jan-2 Feb 1996 Sponsor(s): IEEE Power Eng. Soc.; IEEE Neural Network Council; NSF Price: CCCC 0 7803 3115 X/96/$5.00 ISBN: 0-7803-3115-X DT Conference Article TC Theoretical CY United States LA English AB This paper presents a practical method of solving the power system unit commitment problem by using a genetic algorithm and the Lagrangian relaxation method, making use of the advantages of both. Moreover, the introduction of heuristics simplifies genetic string manipulations which improve computational efficiency. Numerical results have shown that the method is effective in solving the practical unit commitment problem. L8 ANSWER 24 OF 404 INSPEC COPYRIGHT 1997 FIZ KARLSRUHE AN 96:5245715 INSPEC DN A9610-6630H-007 TI Determination of chemical diffusion coefficient of SrFeCo0.5Ox by the conductivity ***relaxation*** ***method*** . AU Ma, B.; Balachandran, U.; Park, J.H. (Energy Technol. Div., Argonne Nat. Lab., IL, USA); Segre, C.U. SO Solid State Ionics, Diffusion & Reactions (15 Jan. 1996) vol.83, no.1-2, p.65-71. 26 refs. Published by: Elsevier Price: CCCC 0167-2738/96/$15.00 CODEN: SSIOD3 ISSN: 0167-2738 SICI: 0167-2738(19960115)83:1/2L.65:DCDC;1-E DT Journal TC Experimental; Theoretical CY Netherlands LA English AB A conductivity relaxation experiment has been conducted on an SrFeCo0.5Ox sample by abruptly changing the oxygen partial pressure in the atmosphere and monitoring the change of conductivity as a function of time. The re-equilibrium process obeys Fick's second law. By fitting the relaxation data to the solution of the diffusion equation with appropriate boundary conditions, we could determine the oxygen chemical diffusion coefficient and the activation energy. The oxygen diffusion coefficient is 8.9*10-7 cm2/s at 900 degrees C and it increases with increase in temperature. Measured activation energy is 0.92 eV, which is slightly lower than that of other oxides in the system SrFe1-xCoxOy. L8 ANSWER 27 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5205427 INSPEC DN B9604-1130B-019; C9604-7410D-099 TI ***Relaxation*** ***methods*** for analogue fault simulation. AU Zwolinski, M. (Dept. of Electron. & Comput. Sci., Southampton Univ., UK) SO 1995 20th International Conference on Microelectronics. Proceedings (Cat. No.95TH8108) New York, NY, USA: IEEE, 1995. p.467-71 vol.2 of 2 vol. x+viii+870 pp. 4 refs. Conference: Nis, Serbia, 12-14 Sept 1995 Sponsor(s): IEEE Electron. Devices Soc Price: CCCC 0 7803 2786 1/95/$4.00 ISBN: 0-7803-2786-1 DT Conference Article TC Theoretical CY United States LA English AB The fault simulation of analogue circuits is an inherently difficult problem because of the lack of a simple fault model and because analogue simulation is itself slow. This paper describes a technique in which faulty and fault-free circuits are simulated together, such that if the terminal voltages of an active device are the same for the faulty and fault-free circuit, the model values calculated for the fault-free simulation are reused in the faulty simulation. A simple example is given in which it is shown that some savings in the CPU time are possible. Suggestions for further development of the algorithm to give substantial CPU savings are given. L8 ANSWER 29 OF 404 INSPEC COPYRIGHT 1997 IEE AN 96:5156791 INSPEC DN A9604-4710-004 TI Assessment of some iterative methods for non-symmetric linear systems arising in computational fluid dynamics. AU Soria, A.; Ruel, F. (Safety Technol. Inst., Comm. of the Eur. Communities, Ispra, Italy) SO International Journal for Numerical Methods in Fluids (30 Dec. 1995) vol.21, no.12, p.1171-200. 26 refs. Published by: Wiley Price: CCCC 0271-2091/95/121171-30 CODEN: IJNFDW ISSN: 0271-2091 SICI: 0271-2091(19951230)21:12L.1171:ASIM;1-I DT Journal TC Theoretical CY United Kingdom LA English AB Various rests have been carried out in order to compare the performances of several methods used to solve the non-symmetric linear systems of equations arising from implicit discretizations of CFD problems, namely the scalar advection-diffusion equation and the compressible Euler equations. The iterative schemes under consideration belong to three families of algorithms: relaxation (Jacobi and Gauss-Seidel), gradient and Newton methods. Two gradient methods have been selected: a Krylov subspace iteration method (GMRES) and a non-symmetric extension of the conjugate gradient method (CGS). Finally, a quasi-Newton method has also been considered (Broyden). The aim of this paper is to provide indications of which appears to be the most adequate method according to the particular circumstances as well as to discuss the implementation aspects of each scheme. L8 ANSWER 32 OF 404 INSPEC COPYRIGHT 1997 IEE AN 95:5089277 INSPEC DN C9512-4140-033 TI A parallel ***relaxation*** ***method*** for quadratic programming problems with interval constraints. AU Sugimoto, T. (Minist. of International Trade & Industry, Tokyo, Japan); Fukushima, M.; Ibaraki, T. SO Journal of Computational and Applied Mathematics (20 June 1995) vol.60, no.1-2, p.219-36. 18 refs. Price: CCCC 0377-0427/95/$09.50 CODEN: JCAMDI ISSN: 0377-0427 Conference: International Meeting on Linear/Nonlinear Iterative Methods and Verification of Solution. Matsuyama, Japan, 6-9 July 1993 DT Conference Article; Journal TC Theoretical CY Netherlands LA English AB Optimization problems with interval constraints are encountered in various fields such as network flows and computer tomography. As these problems are usually very large, they are not easy to solve without taking their sparsity into account. Recently "row-action methods", which originate from the classical Hildreth's method for quadratic programming problems, have drawn much attention, since they are particularly useful for large and sparse problems. Various row-action methods have already been proposed for optimization problems with interval constraints, but they mostly belong to the class of sequential methods based on the Gauss-Seidel and SOR methods. In this paper, we propose a highly parallelizable method for solving those problems, which may be regarded as an application of the Jacobi method to the dual of the original problems. We prove convergence of the algorithm and report some computational results to demonstrate its effectiveness. L8 ANSWER 33 OF 404 INSPEC COPYRIGHT 1997 IEE AN 95:5088386 INSPEC DN B9512-0290P-007; C9512-4170-014 TI On the multigrid waveform ***relaxation*** ***method*** . AU Ta'asan, S. (Dept. of Math., Carnegie Mellon Univ., Pittsburgh, PA, USA); Zhang, H. SO SIAM Journal on Scientific Computing (Sept. 1995) vol.16, no.5, p.1092-104. 13 refs. Price: CCCC 1064-8275/95/$1.50+0.10 CODEN: SJOCE3 ISSN: 1064-8275 DT Journal TC Theoretical CY United States LA English AB The multigrid waveform relaxation method is an efficient method for solving certain classes of time-dependent partial differential equations (PDEs). This paper studies the relationship between this method and the analogous multigrid method for steady-state problems. Using a Fourier-Laplace analysis, practical convergence rate estimates of the multigrid waveform relaxation are obtained. Experimental results show that the analysis yields accurate performance prediction. L8 ANSWER 37 OF 404 INSPEC COPYRIGHT 1997 IEE AN 95:5060888 INSPEC DN A9521-8140G-003 TI Stress ***relaxation*** ***method*** for investigation of softening kinetics in hot deformed steels. AU Karjalainen, L.P. (Dept. of Mech. Eng., Oulu Univ., Finland) SO Materials Science and Technology (June 1995) vol.11, no.6, p.557-65. 30 refs. CODEN: MSCTEP ISSN: 0267-0836 DT Journal TC Experimental CY United Kingdom LA English AB The feasibility of using high temperature stress relaxation to monitor the restoration process in hot deformed austenite has been studied. The stress relaxation technique was applied to determine the kinetics of softening in C-Mn and C-Mn-Nb steels, and the effects of temperature, axisymmetric compressive strain, strain rate, and reheating temperature are demonstrated and the results compared with the predicted values. In particular; the role of niobium in preventing recrystallisation is considered. The results show that the method is able to reveal the progress of static recrystallisation, and that the softening ratio at any given time can be predicted from the recorded relaxation curves. The effects of some particular experimental factors on the results are discussed, such as an applied stress during the softening and the longitudinal temperature gradient present in the specimens. The particular effectiveness of the technique for the investigation of fast restoration processes such as recovery and metadynamic recrystallisation due to instantaneous data acquisition after the deformation stage is emphasised. L8 ANSWER 41 OF 404 INSPEC COPYRIGHT 1997 IEE AN 95:4988305 INSPEC DN A9515-9850-023 TI ***Relaxation*** ***method*** for automatic identification (of galaxies). AU Delbos, C.; Pinon, J.M.; Servigne, S.; Vidal, F. (Inst. Nat. des Sci. Appliquees, Villeurbanne, France); Garnier, R.; Paturel, G. SO Astrophysical Letters & Communications (1995) vol.31, no.1-6, p.91-3. 1 refs. CODEN: ALECE7 ISSN: 0888-6512 Conference: World of Galaxies II. Lyon, France, 5-7 Sept 1994 DT Conference Article; Journal TC Application; Practical CY Switzerland LA English AB In the Lyon-Meudon extragalactic database, LEDA, images are managed together with astrophysical parameters. The probabilistic relaxation method is used to allow an automatic cross-identification between a well-identified galaxy and the corresponding flux enhancement on the image. A test is performed to control the result. L8 ANSWER 44 OF 404 INSPEC COPYRIGHT 1997 IEE AN 95:4919845 INSPEC DN B9505-5240-010 TI Transient analysis of lossy coupled transmission lines in a lossy medium using the waveform ***relaxation*** ***method*** . AU Lau, F.C.M. (Dept. of Electron. Eng., Hong Kong Polytech., Hong Kong); Deeley, E.M. SO IEEE Transactions on Microwave Theory and Techniques (March 1995) vol.43, no.3, p.692-7. 3 refs. Price: CCCC 0018-9480/95/$04.00 CODEN: IETMAB ISSN: 0018-9480 DT Journal TC Theoretical CY United States LA English AB The waveform relaxation method has been shown to be both efficient and accurate when applied to coupled transmission lines with conductor losses. In this paper, the method is generalized to include the dielectric loss surrounding the transmission lines. The distributed loss model assumes that the conductance matrix is approximately diagonal and its product with the resistive matrix is a scalar matrix. Computational results using the model is presented and compared with HSPICE solutions. L8 ANSWER 45 OF 404 INSPEC COPYRIGHT 1997 IEE AN 95:4866237 INSPEC DN A9504-6120-012 TI Molecular dynamics studies in isotropic phase of n-TPEB's by dielectric ***relaxation*** ***method*** . AU Jadzyn, J. (Inst. of Molecular Phys., Polish Acad. of Sci., Poznan, Poland); Legrand, C.; Isaert, N.; Cartier, A.; Bonnet, P.; Czechowski, G.; Zywucki, B. SO Journal of Molecular Liquids (Nov. 1994) vol.62, p.55-63. 13 refs. Price: CCCC 0167-7322/94/$07.00 CODEN: JMLIDT ISSN: 0167-7322 DT Journal TC Theoretical CY Netherlands LA English AB The result of dielectric relaxation measurements (1 kHz/1 GHz) for series of mesogenic molecules CnH2n+1- phi - phi CH2-CH2 phi -NCS, n-TPEB, (n=7/10) in the isotropic phase, have been presented. Two Debye-type bands have been interpreted as a dielectric absorption due to the rotation around the long and short molecular axis. An optimization of the geometry of non-rigid TPEB molecules have been made using a quantum mechanics semi-empirical method PM3. L8 ANSWER 46 OF 404 INSPEC COPYRIGHT 1997 IEE AN 95:4846859 INSPEC DN C9502-1230D-025 TI Modified ***relaxation*** ***method*** for solution of continuous recurrent neural networks. AU Wilamowski, B.M.; Kanarowski, S.M. (Dept. of Electr. Eng., Wyoming Univ., Laramie, WY, USA) SO Proceedings of the 36th Midwest Symposium on Circuits and Systems (Cat. No.93CH3381-1) New York, NY, USA: IEEE, 1993. p.1081-4 vol.2 of 2 vol. xxxv+1565 pp. 9 refs. Conference: Detroit, MI, USA, 16-18 Aug 1993 Sponsor(s): Wayne State Univ.; IEEE Circuits & Syst. Soc Price: CCCC CH3381-1/93/$01.00 ISBN: 0-7803-1760-2 DT Conference Article TC Theoretical CY United States LA English AB The derivation of a modified relaxation algorithm is presented followed by demonstration examples. The algorithm converges very well for continuous recurrent neural networks with both low and high gain neurons. This enables one to simulate recurrent Hopfield networks with both "soft" and "hard" continuous activation functions. The algorithm is suitable for large systems since the computational effort is proportional only to the system size, in contrast to the commonly used Newton-Raphson method where power relationships exist. L8 ANSWER 47 OF 404 INSPEC COPYRIGHT 1997 IEE AN 94:4837619 INSPEC DN B9501-8230-017 TI Environmentally constrained economic dispatch using the LaGrangian ***relaxation*** ***method*** . AU El-Keib, A.A.; Ma, H. (Alabama Univ., Tuscaloosa, AL, USA); Hart, J.L. SO IEEE Transactions on Power Systems (Nov. 1994) vol.9, no.4, p.1723-9. 18 refs. Price: CCCC 0885-8950/94/$04.00 CODEN: ITPSEG ISSN: 0885-8950 DT Journal TC Theoretical CY United States LA English AB This paper presents a general formulation of the environmentally constrained economic dispatch (ECED) problem based on the requirements of Clean Air Act Amendments of 1990 and others which may be imposed by local air quality regulations. The formulation considers multiple NOx constraints and incorporates the utilization of the affected units (those named in the legislation) along with SO2 constraints. It also proposes a new algorithm to solve the problem for large power systems. This algorithm has the ability to handle a large number of various types of linear and nonlinear environmental constraints. It is reliable, and viable for both offline and online applications. Test results on a large size power system demonstrate the possible savings which can be realized by using the algorithm. Details of the problem formulation and the solution technique are given in the paper. L8 ANSWER 50 OF 404 INSPEC COPYRIGHT 1997 IEE AN 94:4806786 INSPEC DN A9424-3325-009 TI Constant- ***relaxation*** ***methods*** for diffusion measurements in the fringe field of superconducting magnets. AU Demco, D.E.; Johansson, A.; Tegenfeldt, J. (Inst. of Chem., Uppsala Univ., Sweden) SO Journal of Magnetic Resonance, Series A (Oct. 1994) vol.110, no.2, p.183-93. 38 refs. Price: CCCC 1064-1858/94/$6.00 CODEN: JMRAE2 ISSN: 1064-1858 DT Journal TC Experimental CY United States LA English AB A number of new NMR methods have been introduced for measuring molecular self-diffusion coefficients in the fringe field of superconducting magnets, avoiding the determination of longitudinal and transverse magnetization relaxation rates. Constant-relaxation methods based on the stimulated-echo product signals allow the determination of both constant and time-dependent diffusion coefficients. A density-operator formalism taking into account phenomenologically the effect of relaxation and diffusion encoding on the Liouville coordinates has been used to introduce and characterize an inhomogeneous mixed echo. This echo corresponds to a spatial and temporal superposition of a conventional spin echo and a stimulated echo. The mixed echo is generated by the action of a pulse sequence based on a stimulated-echo three-pulse sequence with an insertion of a Carr-Purcell-like pulse sequence in the last pulse interval. A constant relaxation method using a Carr-Purcell mixed-echo pulse sequence has been developed. It has proved to be advantageous when T2 is not very small compared to T1. The performance and limitations of these methods are discussed and demonstrated experimentally. L8 ANSWER 51 OF 404 INSPEC COPYRIGHT 1997 IEE AN 94:4766926 INSPEC DN C9411-1250B-003 TI Recognition of handwritten Chinese characters by modified ***relaxation*** ***methods*** . AU An-Bang Wang; Kuo-Chin Fan (Inst. of Comput. Sci. & Electron. Eng., Nat. Central Univ., Chung-Li, Taiwan); Huang, J.S. SO Image and Vision Computing (Oct. 1994) vol.12, no.8, p.509-22. 26 refs. Price: CCCC 0262-8856/94/08/0509-14$10.00 CODEN: IVCODK ISSN: 0262-8856 DT Journal TC Practical; Theoretical CY United Kingdom LA English AB We propose a novel stroke segmentation method and two modified relaxation methods with which to recognize handwritten Chinese characters. The new stroke segmentation method is based on thinning and quadratic equation fit. After stroke segmentation and size normalization, redundant strokes are detected and deleted. With the deletion of redundant strokes, only prominent strokes that must appear in the writing of a character are stored in the database, greatly decreasing the matching time and complexity. The features of each stroke are then extracted. Using the features of a character, two modified relaxation matching methods are introduced to recognize the unknown input character. After relaxation matching, certain rules are devised to detect certain distorted characters, and also to resolve ambiguity when it happens. Some of these distorted characters are reconstructed and their feature vector lists are modified to reflect the change. It is then sent back to the feedback relaxation matching process once again. Experiments are conducted on 300 constrained handwritten characters written by two people; 13 similar characters and 42 distorted characters are also tested to verify the validity of the approach. The success rate for stroke segmentation is 93.3%. Two proposed matching methods are also efficient and suitable for stroke-based Chinese character recognition. The overall recognition rate is 98.7%, without using Rules 2-5 and without considering the abnormal connection and intersection of strokes. L8 ANSWER 58 OF 404 INSPEC COPYRIGHT 1997 IEE AN 94:4617645 INSPEC DN B9404-6140C-253; C9404-1250-153 TI Finding edge in images: a hierarchical ***relaxation*** ***method*** . AU Dingding Chang; Hashimoto, S. (Sch. of Sci. & Eng., Waseda Univ., Tokyo, Japan) SO Transactions of the Society of Instrument and Control Engineers (1993) vol.29, no.12, p.1379-87. 15 refs. CODEN: TSICA9 ISSN: 0453-4654 DT Journal TC Theoretical CY Japan LA English AB Edge features can be used in the scene analysis and computer vision. In this paper, we present a hierarchical relaxation method for detecting edge features in images. The relaxation processes are performed on the pyramid, which is a hierarchical representation about the image. Using multiresolution information about the image, we can change the weighted coefficients by considering the processed results at high hierarchy as a measurement of the local edge features in the image, satisfactory detection can be obtained in all the parts of the image, and convergence speed of the relaxation processes can be improved greatly. This method has the advantage of detection of complete border of the objects in the image. L8 ANSWER 66 OF 404 INSPEC COPYRIGHT 1997 IEE AN 93:4531812 INSPEC DN A9401-8715M-011; C9401-7320-044 TI Divide-and-conquer, pattern matching, and ***relaxation*** ***methods*** in interpretation of 2-D NMR spectra of polypeptides. AU Von-Wun Soo (Dept. of Comput. Sci. & Nat. Tsing Hua Univ., Hsin-Chu, Taiwan); Jan-Fu Hwang; Tung-Bo Chen; Chin Yu SO Journal of Computational Chemistry (Oct. 1993) vol.14, no.10, p.1164-71. 22 refs. Price: CCCC 0192-8651/93/101164-08 CODEN: JCCHDD ISSN: 0192-8651 DT Journal TC Practical; Theoretical CY United States LA English AB One task in the interpretation of the 2-D nuclear magnetic resonance (NMR) spectrum is to assign its signal patterns to their corresponding amino acids in proteins or polypeptides. To carry out this task of interpretation, one requires sufficient chemical knowledge and expertise to reason from a set of highly noisy data. The authors present a system called RUBIDIUM (a Rule-Based Identification in 2-D NMR Spectrum) to formulate the expertise and automate the process of interpretation. Given a protein or polypeptide with a known amino acid sequence and the 2-D NMR spectra (both COSY and NOESY), RUBIDIUM yields plausible assignments of lines that account for most signals observed in the spectrum and conform to prior chemical knowledge. Rules of pattern matching are used to detect plausible signal patterns. The expertise of the sequence-specific assignment task is formulated to assign a signal pattern to amino acids. To cope with ambiguities and noise, RUBIDIUM adopts various low-level data preprocessing techniques, the strategy of divide and conquer, and the relaxation technique to decrease the complexity and recover from overconstrained conditions. The polypeptides oxytocin and vasopressin are used to illustrate the performance of RUBIDIUM. L8 ANSWER 69 OF 404 INSPEC COPYRIGHT 1997 IEE AN 93:4510863 INSPEC DN A9323-0720-002 TI Temperature dependence measurements of thermal parameters of solid samples by the ***relaxation*** ***method*** . AU Budke, O.; Dieska, P. (Dept. of Phys., Slovak Tech. Univ., Bratislava, Slovakia) SO International Journal of Heat and Mass Transfer (Oct. 1993) vol.36, no.15, p.3869-72. 7 refs. Price: CCCC 0017-9310/93/$6.00+0.00 CODEN: IJHMAK ISSN: 0017-9310 DT Journal TC Theoretical CY United Kingdom LA English AB A generalization of the relaxation method (Budke and Dieska, 1985) has been elaborated. While an application of the relaxation method requires the sample holder temperature to be constant in time, this generalized version admits a polynomial change of the sample holder temperature. Such a temperature course is a very common and realistic one at temperature dependence measurements of thermal parameters. L8 ANSWER 71 OF 404 INSPEC COPYRIGHT 1997 IEE AN 93:4476853 INSPEC DN B9310-1160-003 TI Use of a Laplace-transform ***relaxation*** ***method*** for the analysis of nonlinear electric circuits. AU Ichikawa, S.; Tada, H. (Fac. of Eng., Kyoto Univ., Japan) SO Electronics and Communications in Japan, Part 3 (Fundamental Electronic Science) (Dec. 1992) vol.75, no.12, p.11-20. 5 refs. Price: CCCC 1042-0967/92/0012-0011 CODEN: ECJSER ISSN: 1042-0967 DT Journal TC Theoretical CY United States LA English AB The relaxation method is suitable for analysis of large-scale circuits such as those simulating VLSI circuits. Complex frequency domain analysis by means of the Laplace transform is carried out. Semiconducting elements such as transistors of the VLSI circuits exhibit nonlinear characteristics. Thus, the differential equations to be used in the relaxation method must be nonlinear. In some cases, the properties of nonlinear elements are given not by analytic functions but by a series of discrete numerical values such as observed data. To express the nonlinearity of these elements, multidimensional interpolation formulas are used and practical computer algorithms for solving them are derived. The analysis of the conditions of convergence of the relaxation method shows that the proposed algorithm is applicable to circuits which operate in both stable and unstable domains, such as oscillators. L8 ANSWER 78 OF 404 INSPEC COPYRIGHT 1997 IEE AN 93:4369351 INSPEC DN B9305-8110D-001 TI An application of the Lagrangean ***relaxation*** ***method*** to unit commitment scheduling in a power generation system with pumped-storage units. AU Kim, S. (Dept. of Manage. Sci. & Technol. Taejon, South Korea); Rhee, M. SO Computers & Industrial Engineering (Jan. 1993) vol.24, no.1, p.69-79. 27 refs. Price: CCCC 0360-8352/93/$6.00+0.00 CODEN: CINDDL ISSN: 0360-8352 DT Journal TC Theoretical CY United Kingdom LA English AB The Lagrangean relaxation method is applied to the unit commitment problem of a power generation system with pumped-storage units. The shortest path algorithm is used for the subproblem for each thermal unit and the minimal cost flow algorithm is used for each pumped-storage unit. A method for finding a better feasible solution from a solution of a relaxed problem is presented. A real Korean power generation system with 39 thermal units and one pumped-storage unit is tested. The authors considered 168 planning hours and were able to find a near optimal solution (within 0.5% of optimal) consuming a reasonable amount of CPU time. L8 ANSWER 88 OF 404 INSPEC COPYRIGHT 1997 IEE AN 92:4276811 INSPEC DN A9224-4740-002 TI Iterative methods for stationary solutions to the steady-state compressible Navier-Stokes equations. AU Sjogreen, B. (Dept. of Sci. Comput., Uppsala Univ., Sweden) SO Computers & Fluids (Oct. 1992) vol.21, no.4, p.627-45. 15 refs. Price: CCCC 0045-7930/92/$5.00+0.00 CODEN: CPFLBI ISSN: 0045-7930 DT Journal TC Theoretical CY United Kingdom LA English AB Numerical experiments are presented for the solution of the steady-state compressible Navier-Stokes equations. One test problem is fixed supersonic flow past a double ellipse, and the various solution methods studied. The problem is discretized using Osher's scheme, first- and second-order accurate. The fastest convergence to steady state is obtained using Newton's method. Simplifications of Newton's method based on domain decomposition are shown to perform well, whereas line relaxation methods meet with difficulties. L8 ANSWER 96 OF 404 INSPEC COPYRIGHT 1997 IEE AN 92:4185303 INSPEC DN A9216-4110D-010; B9208-5120-012 TI The use of a ***relaxation*** ***method*** to calculate the 3D magnetic field contribution of an iron yoke. AU Caspi, S.; Helm, M.; Laslett, L.J. (Lawrence Berkeley Lab., CA, USA) SO IEEE Transactions on Magnetics (March 1992) vol.28, no.2, p.1096-8. 2 refs. Price: CCCC 0018-9464/92/$03.00 CODEN: IEMGAQ ISSN: 0018-9464 Conference: Computation of Electromagnetic Fields (COMPUMAG). Sorrento, Italy, 7-11 July 1991 Sponsor(s): IEEE DT Conference Article; Journal TC Theoretical CY United States LA English AB A computational procedure has been developed for calculating the 3-D field produced by an axisymmetric iron yoke of high permeability in the presence of a system of conductors. The procedure is particularly applicable to the end regions of multipole magnets of the sort used in particle accelerators. The field produced by the conductors is calculated using the Biot-Savart law. If one solves the appropriate individual differential equations for specified scalar potential functions throughout the iron-free region, with the proper applied boundary condition for the scalar potential of each harmonic number, one will achieve upon summation the appropriate potential function to describe the field contribution of the surrounding high-permeability iron. L8 ANSWER 99 OF 404 INSPEC COPYRIGHT 1997 IEE AN 92:4152884 INSPEC DN A9212-4730-015 TI Flow of a viscous fluid past a flexible membrane at low Reynolds numbers. AU Yamamoto, K.; Okada, M.; Kameyama, J. (Dept. of Mech. Eng., Fac. of Eng., Okayama Univ., Japan) SO Fluid Dynamics Research (April 1992) vol.9, no.5-6, p.289-99. 13 refs. Price: CCCC 0169-5983/92/$3.75 CODEN: FDRSEH ISSN: 0169-5983 DT Journal TC Theoretical CY Netherlands LA English AB The numerical calculation of a steady two-dimensional viscous flow past a flexible membrane is treated. Both edges of the membrane are fixed in the flow and its chord is set normal to the flow. The Navier-Stokes equation in terms of the stream function and the vorticity is transformed to the body fitted coordinate system. The numerical calculations, based on a finite difference method and relaxation method, are carried out for several values of the membranes tension for cases when the Reynolds numbers are 5, 10 and 20. It is found that two different shapes of the membranes are possible at a given value of tension and Reynolds number: one with a small deformation, and the other with a large deformation. Two vortices appear in the concave region of the membrane if its deformation increases beyond a certain extent. L8 ANSWER 101 OF 404 INSPEC COPYRIGHT 1997 IEE AN 92:4140055 INSPEC DN A9211-4740K-003 TI An improved upwind finite volume ***relaxation*** ***method*** for high speed viscous flows. AU Taylor, A.C., III (Dept. of Mech. Eng. & Mech., Old Dominion Univ., Norfolk, VA, USA); Wing-fai Ng; Walters, R.W. SO Journal of Computational Physics (March 1992) vol.99, no.1, p.159-68. 22 refs. Price: CCCC 0021-9991/92/$3.00 CODEN: JCTPAH ISSN: 0021-9991 DT Journal TC Theoretical CY United States LA English AB An improved upwind relaxation algorithm for the Navier-Stokes equations is presented, and results are given from the application of the method to two test problems, including (1) a shock/boundary layer interaction on a flat plate (Minfinity =2.0) and (2) a high-speed inlet (Minfinity =5.0). The technique is restricted to high-speed (i.e., supersonic/hypersonic) viscous flows. The new algorithm depends on a partitioning of the global domain into regions or sub-domains, where a relatively thin 'elliptic' region is identified near each solid wall boundary, and the remainder of the flowfield is identified to be a single larger 'hyperbolic' (i.e., hyperbolic/parabolic in the streamwise direction) region. A direct solution procedure by lower/upper factorization is applied to the elliptic region, the results of which are then coupled to a standard line Gauss-Seidel relaxation sweep across the entire domain in the primary flow direction. L8 ANSWER 125 OF 404 INSPEC COPYRIGHT 1997 IEE AN 91:3784657 INSPEC DN A91013094 TI A new approach to the borehole temperature ***relaxation*** ***method*** . AU Wilhelm, H. (Geophys. Inst., Karlsruhe Univ., West Germany) SO Geophysical Journal International (Nov. 1990) vol.103, no.2, p.469-81. 20 refs. ISSN: 0956-540X DT Journal TC Practical CY United Kingdom LA English AB The borehole temperature relaxation method is used to determine in situ thermal properties of rock by a thermal disturbance in an uncased borehole. The conventional application of this method is based on the assumption that the heat flow through the borehole wall is constant in time and only a function of depth during the disturbance phase. The new approach described in this paper offers a solution to the problem which does not refer directly to the thermal history during the disturbance phase. It is only based on temperature measurements during the relaxation phase when the disturbance fades away by conduction. L8 ANSWER 126 OF 404 INSPEC COPYRIGHT 1997 IEE AN 91:3778580 INSPEC DN A91013447; B91006258 TI A ***relaxation*** ***method*** for integral inversion applied to HF radar measurement of the ocean wave directional spectrum. AU Wyatt, L.R. (Dept. of Appl. & Comput. Math., Sheffield Univ., UK) SO International Journal of Remote Sensing (Aug. 1990) vol.11, no.8, p.1481-94. 22 refs. Price: CCCC 0143-1161/90/$3.00 CODEN: IJSEDK ISSN: 0143-1161 DT Journal TC Practical; Theoretical CY United Kingdom LA English AB The Chahine-Twomey relaxation method for inversion of the atmospheric radiative transfer equation is extended to provide an inverse solution to Barrick's equation describing second order scatter of high frequency (HF) radio waves from the ocean surface. The success of the method is demonstrated using synthesised radar Doppler spectra obtained by solving the direct problem with wave buoy directional spectrum measurements. Wave buoy measurements are limited in the range of directional characteristics that can be measured. The results presented suggest that HF radar is capable of providing a more general measurement of the directional spectrum. L8 ANSWER 136 OF 404 INSPEC COPYRIGHT 1997 IEE AN 90:3707065 INSPEC DN B90058649; C90056028 TI Lagrangian ***relaxation*** ***method*** for long-term unit commitment. AU Aoki, K.; Nara, K.; Satoh, T.; Itoh, M. (Dept. of Electr. & Syst. Eng., Hiroshima Univ., Japan) SO Power Systems and Power Plant Control 1989. Selected Papers from the IFAC Symposium Editor(s): Uhi Ahn Oxford, UK: Pergamon, 1990. p.123-8 of xvi+545 pp. 8 refs. Conference: Seoul, South Korea, 22-25 Aug 1989 Sponsor(s): IFAC SBN: 0-08-037039-x DT Conference Article TC Theoretical CY United Kingdom LA English AB The authors present a new method for large-scale long-term unit commitment problem composed of three types of generating units. In the proposed unit commitment algorithm, the transmission loss is expressed as a quadratic function of generator outputs. In the demand increasing period in the morning, the planning period (one hour) should be divided into shorter periods such as a half an hour of fifteen minutes, and the ramping rate constraints should be imposed on generator outputs. Since the unit commitment problem (primal problem) is formulated as a large-scale mixed-integer programming problem, the Lagrangian relaxation method is employed to solve the problem efficiently. L8 ANSWER 137 OF 404 INSPEC COPYRIGHT 1997 IEE AN 90:3690713 INSPEC DN A90110333 TI A method for solving three-dimensional viscous incompressible flows over slender bodies. AU Rosenfeld, M.; Israeli, M.; Wolfshtein, M. (Technion-Israel Inst. of Technol., Haifa, Israel) SO Journal of Computational Physics (June 1990) vol.88, no.2, p.255-83. 21 refs. Price: CCCC 0021-9991/90/$3.00 CODEN: JCTPAH ISSN: 0021-9991 DT Journal TC Theoretical CY United States LA English AB A marching iterative method for solving the three-dimensional incompressible and steady reduced Navier-Stokes equations in general orthogonal coordinate systems is described with the velocity and the pressure as dependent variables. The coupled set of the linearized finite-difference continuity and momentum equations are solved iteratively without any splitting or factorization errors. Each iteration consists of spatial marching from the upstream boundary to the downstream boundary. The discrete continuity and the two linearized crossflow momentum equations are satisfied at each marching step, even when the mainstream momentum equation is not converged. This solution procedure is equivalent to the solution of a single Poisson-like equation by the successive plane over relaxation method, while other available solution methods employ a Jacobi-type iterative scheme and therefore are less efficient. Several properties of the numerical method have been assessed through a series of tests performed on the laminar incompressible flow over prolate spheroids at intermediate incidence. L8 ANSWER 145 OF 404 INSPEC COPYRIGHT 1997 IEE AN 90:3632363 INSPEC DN B90034989; C90036810 TI Availability of nonlinear ***relaxation*** ***method*** for network analysis in the frequency domain. AU Kawashima, T.; Hagiwara, Y.; Asai, H. (Fac. of Eng., Shizuoka Univ., Hamamatsu, Japan) SO Transactions of the Institute of Electronics, Information and Communication Engineers A (Dec. 1989) vol.J72A, no.12, p.2061-4. 4 refs. CODEN: DJTAER ISSN: 0913-5707 DT Journal TC Theoretical; Experimental CY Japan LA Japanese AB Describes the availability of the nonlinear relaxation method for the solution of the determining equation given by the harmonic balance method for the frequency domain network analysis. The authors show that their algorithm saves CPU time and memory capacity, compared with the previous one. L8 ANSWER 155 OF 404 INSPEC COPYRIGHT 1997 IEE AN 90:3521419 INSPEC DN A90007776 TI Application of thermal conductivity measurement by the ***relaxation*** ***method*** to crystallization kinetics of glassy As2Se3+1 mol.% In. AU Budke, O. (Dept. of Phys., Slovak Tech. Univ., Bratislava, Czechoslovakia); Svec, P. SO Physica Status Solidi A (16 Sept. 1989) vol.115, no.1, p.143-8. 13 refs. CODEN: PSSABA ISSN: 0031-8965 DT Journal TC Experimental CY German Democratic Republic LA English AB The use of a recently developed nonstationary relaxation method of measuring thermal conductivity lambda of solids for monitoring crystallization kinetics of chalcogenide glasses has been analyzed. Time dependences lambda (t) upon crystallization have been obtained for isothermally annealed glasses As2Se3+1 mol.% In and the models for calculation of degree of crystallinity and evaluation of kinetic parameters of crystallization have been presented. Activation energy of crystallization, dimensionality of grain growth, and character of nucleation have been determined and the character of kinetic behavior has been discussed with consideration to possible autocatalysis of the process. => d bib ab 156,158,170,174,177,200,211,212,221,224,225,230,240,243,246,258,278,281,283,285,290,300,304,306,314,317,327,328,340 L8 ANSWER 156 OF 404 INSPEC COPYRIGHT 1997 IEE AN 89:3495790 INSPEC DN C89066511 TI Solution of ordinary differential equations by waveform ***relaxation*** ***methods*** . AU Skelboe, S. (Dept. of Comput. Sci., Copenhagen Univ., Denmark) SO Aspects of Computation on Asynchronous Parallel Processors. Proceedings of the IFIP WG 2.5 Working Conference Editor(s): Wright, M. Amsterdam, Netherlands: North-Holland, 1989. p.225 of xi+271 pp. 0 refs. Conference: Stanford, CA, USA, 22-26 Aug 1988 Sponsor(s): Lawrence Livermore Nat. Lab.; Appl. Dynamics Int.; Stanford Univ ISBN: 0-444-87310-4 DT Conference Article TC Theoretical CY Netherlands LA English AB Summary form only given, as follows. Waveform relaxation methods have proved efficient for the simulation of digital circuits using parallel computers. The author describes the method and reports on some of the research activities in this area including: application of the Gauss-Seidel method on parallel computers; stability properties of multirate integration formulas; and application of waveform relaxation to chemical process simulation. L8 ANSWER 158 OF 404 INSPEC COPYRIGHT 1997 IEE AN 89:3470743 INSPEC DN A89120540 TI Numerical simulation of laminar incompressible viscous flow with extremely thin finite elements near the boundaries. AU D'Errico, M.A. CS Inst. Nat. Recherche Inf. Autom., Le Chesnay, France NR 997 SO Feb. 1989. 29 pp. 9 refs. DT Report TC Theoretical CY France LA French AB Viscous and lamina flow simulations are a source of problems at very high Reynolds number (Re) because of the boundary layers. Extremely thin discretization grids are needed in the perpendicular direction to the boundary layer and that produces a bad, or at least mediocre, conditioning of the linear systems. The author does not propose a new approximation in order to solve the problem, but a new way of resolving the linear system that arises from a finite element discretization of the nonstationary, incompressible and laminar Navier-Stokes equations. It is a simple idea that consists in changing the method of resolution in the boundary layer by a block relaxation method, adapted to physics, that imitates the method of resolution of the parabolic Prandtl boundary layer equations, while in the remaining domain a Cholesky or conjugate gradient method is employed. The global linear system is solved by blocks. The first corresponds to the boundary layer and wake; the second corresponds to the remaining domain. The author obtained better results on a wing profile at Reynolds number 100000 because this method seems not to propagate the round off errors due to the bad conditioning of the global linear system. L8 ANSWER 170 OF 404 INSPEC COPYRIGHT 1997 IEE AN 89:3321079 INSPEC DN A89029184; C89023068 TI An adaptive dynamic ***relaxation*** ***method*** for nonlinear problems. AU Shizhong Qiang (Dept. of Civil Eng., Southwestern Jiaotong Univ., Emei, China) SO Computers and Structures (1988) vol.30, no.4, p.855-9. 9 refs. Price: CCCC 0045-7949/88/$3.00+0.00 CODEN: CMSTCJ ISSN: 0045-7949 DT Journal TC Practical; Theoretical CY United Kingdom LA English AB Outlines the so-called dynamic relaxation method (DRM) which is found to be suitable in analyses of both geometrical and material nonlinearities using personal computers, and discuss an approach recently developed at SWJT for the automatic selection of iteration parameters in the DRM. The solution of a nonlinear truss-spring, the analysis of plate bending problems with large deflections under transverse loading, and the calculation of the ultimate load of plates under an in-plane load, using DRM with personal computers, are described. L8 ANSWER 174 OF 404 INSPEC COPYRIGHT 1997 IEE AN 89:3264002 INSPEC DN C89000789 TI Lagrangian ***relaxation*** ***methods*** solving the minimum fleet size multiple traveling salesman problem with time windows. AU Desrosiers, J.; Sauve, M.; Soumis, F. (Ecole des Hautes Etudes Commerciales, Montreal, Que., Canada) SO Management Science (Aug. 1988) vol.34, no.8, p.1005-22. 36 refs. Price: CCCC 0025-1909/88/3408-1005$01.25 CODEN: MSCIAM ISSN: 0025-1909 DT Journal TC Theoretical CY United States LA English AB Considers the problem of finding the minimum number of vehicles required to visit once a set of nodes subject to time window constraints, for homogeneous fleet of vehicles located at a common depot. This problem can be formulated as a network flow problem with additional time constraints. The paper presents an optimal solution approach using the augmented Lagrangian method. Two Lagrangian relaxations are studied. In the first one, the time constraints are relaxed producing network subproblems which are easy to solve, but the bound obtained is weak. In the second relaxation, constraints requiring that each node be visited are relaxed producing shortest path subproblems with time window constraints and integrality conditions. The bound produced is always excellent. Numerical results for several actual school busing problems with up to 223 nodes are discussed. Comparisons with a set partitioning formulation solved by column generation are given. L8 ANSWER 177 OF 404 INSPEC COPYRIGHT 1997 IEE AN 88:3235109 INSPEC DN B88064577 TI Waveform ***relaxation*** ***method*** . AU Urahama, K. (Fac. of Eng., Kyushu Univ., Fukuoka, Japan) SO Journal of the Institute of Electronics, Information and Communication Engineers (Feb. 1988) vol.71, no.2, p.145-7. 21 refs. CODEN: DJTGEB ISSN: 0373-6121 DT Journal TC Application; Experimental CY Japan LA Japanese AB The waveform relaxation method is a repetitive method of the initialization problem for the algebraic/differential equation system, which is similar to Picard's consecutive simulation, the method to apply the Newton method to differential equations, etc. The waveform relaxation method has lately been proved to be effective particularly for simulation of the MOS digital circuit. The multirate integration method is effective for transient analysis of the circuit. In the waveform relaxation method, multirate integration is carried in a natural form. The author describes the convergence of the waveform relaxation method in transient analysis of the MOS digital circuit and high-speed simulation techniques. L8 ANSWER 200 OF 404 INSPEC COPYRIGHT 1997 IEE AN 87:2965207 INSPEC DN A87113750 TI Applications of exponential ***relaxation*** ***methods*** for corrosion studies and corrosion rate measurement. AU Lakshminarayanan, V. (Raman Res. Inst., Bangalore, India); Rajagopalan, S.R. SO Proceedings of the Indian Academy of Sciences, Chemical Sciences (Oct. 1986) vol.97, no.3-4, p.465-77. 6 refs. CODEN: PIAADM ISSN: 0370-0089 DT Journal TC Theoretical CY India LA English AB Investigations on the use of an exponential relaxation technique for studying corrosion systems are reported. The polarisation resistance and the double layer capacitance of corrosion systems can be obtained by the small amplitude exponential relaxation technique (SAERT). The rate of corrosion can be measured by the large amplitude exponential relaxation technique (LAERT). This technique yields an 'accelerated Tafel plot' only when the charging current is negligible, which is seldom so. Methods for correcting for double layer charging are described. Double layer capacitance as a function of potential is obtained from LAERT. Therefore it can be used for studies on inhibitors. The utility of LAERT for corrosion systems with only one of the conjugate reactions under activation control is established. The effect of series resistance (Re) is discussed and an in situ method for its determination is described. A procedure for correcting the experimental data for errors due to Re is given. L8 ANSWER 211 OF 404 INSPEC COPYRIGHT 1997 IEE AN 87:2860637 INSPEC DN A87051021 TI Multiple grid and Osher's scheme for the efficient solution of the steady Euler equations. AU Hemker, P.W.; Spekreijse, S.P. (Centrum voor Wiskunde en Inf., Amsterdam, Netherlands) SO Applied Numerical Mathematics (Dec. 1986) vol.2, no.6, p.475-93. 22 refs. Price: CCCC 0168-9274/86/$3.50 CODEN: ANMAEL ISSN: 0168-9274 DT Journal TC Theoretical; Experimental CY Netherlands LA English AB An iterative method is developed for the solution of the steady Euler equations for inviscid flow. The system of hyperbolic conservation laws is discretized by a finite-volume Osher-discretization. The iterative method is a multiple grid (FAS) iteration with symmetric Gauss-Seidel (SGS) as a relaxation method. Initial estimates are obtained by full multigrid (FMG). In the pointwise relaxation the equations are kept in block-coupled form and local linearization of the equations and the boundary conditions is considered. The efficient formulation of Osher's discretization of the 2-D nonisentropic steady Euler equations and its linearization is presented. The efficiency of FAS-SGS iteration is shown for a transonic model problem. It appears that, for the problem considered, the rate of convergence is almost independent of the grid size and that for all mesh sizes the discrete system is solved up to truncation error accuracy in only a few (2 or 3) iteration cycles. L8 ANSWER 212 OF 404 INSPEC COPYRIGHT 1997 IEE AN 87:2845023 INSPEC DN C87021805 TI An introduction to ***relaxation*** ***methods*** . AU Williams, G. (BYTE, Peterborough, NH, USA) SO BYTE (Jan. 1987) vol.12, no.1, p.111-14, 116, 118, 120, 122, 124. 0 refs. CODEN: BYTEDJ ISSN: 0360-5280 DT Journal TC Theoretical CY United States LA English AB A numeric technique called the relaxation method is very useful in solving such matters as systems of simultaneous equations. The author concentrates on the solution of two-dimensional systems that can be described by Poisson's equation. He focuses on a special case, Laplace's equation. L8 ANSWER 221 OF 404 INSPEC COPYRIGHT 1997 IEE AN 86:2730070 INSPEC DN A86101541 TI A direct ***relaxation*** ***method*** for calculating eigenfunctions and eigenvalues of the Schrodinger equation on a grid. AU Kosloff, R. (Dept. of Phys. Chem., Hebrew Univ., Jerusalem, Israel); Tal-Ezer, H. SO Chemical Physics Letters (13 June 1986) vol.127, no.3, p.223-30. 23 refs. Price: CCCC 0009-2614/86/$03.50 CODEN: CHPLBC ISSN: 0009-2614 DT Journal TC Theoretical CY Netherlands LA English AB Eigenfunctions and eigenvalues of the Schrodinger equation are determined by propagating the Schrodinger equation in imaginary time. The method is based on representing the Hamiltonian operation on a grid. The kinetic energy is calculated by the Fourier method. The propagation operator is expanded in a Chebychev series. Excited states are obtained by filtering out the lower states. Comparative examples include: eigenfunctions and eigenvalues of the Morse oscillator, the Henon-Heiles system and weakly bound states of He on a Pt surface. L8 ANSWER 224 OF 404 INSPEC COPYRIGHT 1997 IEE AN 86:2667490 INSPEC DN A86063383 TI A ***relaxation*** ***method*** for steady Navier-Stokes equations, based on flux-vector splitting. AU Dick, E. (Dept. of Machinery, State Univ. of Ghent, Belgium) SO Numerical Methods in Laminar and Turbulent Flow. Proceedings of the Fourth International Conference Editor(s): Taylor, C.; Olson, M.D.; Gresho, P.M.; Habashi, W.G. Swansea, UK: Pineridge Press, 1985. p.527-38 vol.1 of 2 vol. 1851 pp. 4 refs. Conference: Swansea, UK, 9-12 July 1985 Sponsor(s): US Office Naval Res. ISBN: 0-906674-43-3 DT Conference Article TC Theoretical CY United Kingdom LA English AB Using the example of Cauchy-Riemann equations, the flux-vector splitting method is illustrated for systems of first order equations. It is shown that for this linear elliptic system of equations, flux-vector splitting combined with upwind differencing results in discrete equations which can be solved by relaxation methods. It is shown how the same splitting can be used on the hybrid first order (subprincipal) part of the steady Navier-Stokes equations in primitive variable form. By the use of central difference discretisations on the second order (principal) part, the resulting set of discrete equations can be solved by relaxation methods. A computational example on a backward facing step problem is given. L8 ANSWER 225 OF 404 INSPEC COPYRIGHT 1997 IEE AN 86:2653230 INSPEC DN B86027038; C86025933 TI Application of the ***relaxation*** ***method*** to analysis of DC nonlinear networks. AU Tadeusiewicz, M. (Inst. of Principles of Electr. Eng., Tech. Univ., Lodz, Poland) SO Modelling, Simulation & Control A (1984) vol.1, no.3, p.9-16. 9 refs. CODEN: MSCAE2 ISSN: 0761-2508 DT Journal TC Theoretical CY France LA English AB The application of the relaxation method to computer-aided analysis of nonlinear networks is discussed. For a certain class of DC nonlinear networks, the sufficient conditions under which the relaxation sequence is convergent to a unique solution for each initial guess are formulated. The diode-transistor networks are discussed and a numerical example is demonstrated. L8 ANSWER 230 OF 404 INSPEC COPYRIGHT 1997 IEE AN 86:2588411 INSPEC DN B86007690; C86008145 TI A block ***relaxation*** ***method*** for the three-dimensional Poisson equation. AU Huang Duo (Comput. Center, Acad. Sinica, China) SO Mathematica Numerica Sinica (1985) vol.7, no.3, p.332-6. 6 refs. CODEN: JSUXDP ISSN: 0254-7791 DT Journal TC Theoretical CY China LA Chinese AB A block relaxation method is proposed for the three-dimensional Poisson equation on the basis of a cyclic reduction method. Its convergence is analysed and a formula for determining the optimum relaxation factor is given. L8 ANSWER 240 OF 404 INSPEC COPYRIGHT 1997 IEE AN 85:2475705 INSPEC DN C85031615 TI A Lagrangean- ***relaxation*** ***method*** for the constrained assignment problem. AU Aggarwal, V. (Dept. of Manage. & Syst., Washington State Univ., Pullman, WA, USA) SO Computers & Operations Research (1985) vol.12, no.1, p.97-106. 14 refs. Price: CCCC 0305-0548/85$3.00+.00 CODEN: CMORAP ISSN: 0305-0548 DT Journal TC Theoretical CY United Kingdom LA English AB This paper addresses the problem of finding a minimal weight assignment subject to a knapsack-type constraint. It develops a two-stage algorithm based on the Lagrangean-relaxation formulation of this problem. The first stage obtains the optimal Lagrange multiplier in a polynomial effort by generating the efficient frontier in a bicriteria framework. The second stage uses this information to zero in on the optimal solution in a relatively lower depth of search in the ordered-generation-of-assignments framework. The algorithm is supported by a numerical example and its advantages over other schemes are shown. L8 ANSWER 243 OF 404 INSPEC COPYRIGHT 1997 IEE AN 85:2448430 INSPEC DN A85058371 TI Measurement of thermal parameters of small plane-parallel samples by a ***relaxation*** ***method*** . AU Budke, O.; Dieska, P. (Dept. of Phy., Electrotech., Slovak Tech. Univ., Bratislava, Czechoslovakia) SO Acta Physica Slovaca (1985) vol.35, no.1, p.27-39. 2 refs. CODEN: APSVCO ISSN: 0323-0465 DT Journal TC Experimental CY Czechoslovakia LA English AB A non-stationary method for measuring thermal conductivity and thermal diffusivity of small plane-parallel samples (5*5*1 mm3) is developed. The principle of the method consists in measuring the time dependence of the temperature of a plane heat source heated by a constant power during a finite time interval. The heat capacity of the source is taken into account in the formulation of the problem. A model is proposed to estimate a parasitical heat flow through the lead-in wires of the heat source and the wires of the thermocouple used for measuring the temperature of the heat source. The method is suitable for a quick measuring of the temperature dependence of thermal parameters. L8 ANSWER 246 OF 404 INSPEC COPYRIGHT 1997 IEE AN 85:2404651 INSPEC DN C85012851 TI A case for ***relaxation*** ***methods*** . AU Kumar, G.S. (Sch. of Bus. Adm., Tennessee Univ., Martin, TN, USA) SO Proceedings of the 16th Annual Meeting of the American Institute for Decision Sciences Atlanta, GA, USA: American Inst. Decision Sci, 1984. p.682 of xvii+817 pp. Microfiche Conference: Toronto, Ont., Canada, 5-7 Nov 1984 DT Conference Article TC Theoretical CY United States LA English AB Summary form only given, as follows. Many practical problems can be reduced to finding a point of a polyhedron. Relaxation methods solve the problem by successively finding points of polyhedrons containing the polyhedron of interest. The authors discuss the advantages of using iterative methods for large scale linear programs and survey some of the relaxation methods. L8 ANSWER 258 OF 404 INSPEC COPYRIGHT 1997 IEE AN 84:2178142 INSPEC DN A84013606 TI ***Relaxation*** ***methods*** in investigations of transport processes. AU Buevich, Yu.A.; Yasnikov, G.P. SO Journal of Engineering Physics (March 1983) vol.44, no.3, p.340-53. 131 refs. CODEN: JEPHAL ISSN: 0022-0841 Translation of: Inzhenerno-Fizicheskii Zhurnal (March 1983) vol.44, no.3, p.489-504. 131 refs. CODEN: INFZA9 ISSN: 0021-0285 DT Journal; Translation Abstracted TC Theoretical CY Byelorussian SSR; USSR; United States LA English AB In spite of the large variety of existing transport processes they all have one fundamental property in common: these processes strive to neutralize external actions that take a system out of the equilibrium state. Any physical system has some inertia, related to internal processes specific to the system. Such processes are activated with breakdown of equilibrium and are characterized by their own internal variables. The approach of the system to equilibrium, which results in the observed transport processes, can be viewed as a collection of relaxation processes for these internal variables. The authors limit their analysis to the relaxation formalism of nonequilibrium thermodynamics, and they briefly analyze its relation to the methods of the theory of dynamic systems. L8 ANSWER 278 OF 404 INSPEC COPYRIGHT 1997 IEE AN 81:1752235 INSPEC DN B81044945; C81031168 TI Resolution of the bilinear programming problem via a ***relaxation*** ***method*** . AU Chagoya-Guzman, A.; Fonlupt, J. (Lab. d'Informatique et de Math. Appl., Grenoble, France) SO Methods of Operations Research (1981) vol.40, p.59-62. 5 refs. CODEN: MEORDE ISSN: 0078-5318 Conference: Vth Symposium on Operations Research. Cologne, West Germany, 25-27 Aug 1980 DT Conference Article; Journal TC Theoretical CY Germany, Federal Republic of LA English AB The bilinear programming problem (BPP) may be defined in the following form: v=min(v(x,y)=++; x epsilon K1, y epsilon K2) where K1=(x>or=0; Ax=e) K2=(y>or=0; By=f) are two polytopes. The goal is to find the global optimum (x,y) and the value v=v(x,y) of (BPP). Special methods for nonconvex problems are needed. L8 ANSWER 281 OF 404 INSPEC COPYRIGHT 1997 IEE AN 81:1722606 INSPEC DN C81024877 TI The Lagrangian ***relaxation*** ***method*** for solving integer programming problems. AU Fisher, M.L. (Univ. of Pennsylvania , Philadelphia, PA, USA) SO Management Science (Jan. 1981) vol.27, no.1, p.1-18. 46 refs. CODEN: MSCIAM ISSN: 0025-1909 DT Journal TC Theoretical CY United States LA English AB Many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints. Dualizing the side constraints produces a Lagrangian problem that is easy to solve and whose optimal value is a lower bound (for minimization problems) on the optimal of the original problem. The Lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm. This approach has led to dramatically improved algorithms for a number of important problems in the areas of routing, location, scheduling, assignment and set covering. The paper is a review of Lagrangian relaxation based on what has been learned in the last decade. L8 ANSWER 283 OF 404 INSPEC COPYRIGHT 1997 IEE AN 81:1694822 INSPEC DN B81029190 TI ***Relaxation*** ***methods*** in digital image segmentation. AU Gerbrands, J.J. (Tech. Hogeschool Delft, Delft, Netherlands) SO Tijdschrift van het Nederlands Elektronica- en Radiogenootschap (1981) vol.46, no.1, p.11-16. 11 refs. CODEN: NERTA9 ISSN: 0374-3853 DT Journal TC Theoretical CY Netherlands LA Dutch AB Probabilistic relaxation label procedures are discussed in the context of low-level image segmentation. Two examples are discussed in detail. The first is the reinforcement of edges as proposed by Schachter et al. (1977). The second example deals with image segmentation by clustering in the feature domain followed by relaxation in the spatial domain. The features used are gray-level and texture. L8 ANSWER 285 OF 404 INSPEC COPYRIGHT 1997 IEE AN 81:1673539 INSPEC DN A81042064 TI On a ***relaxation*** ***method*** for calculating two dimensional transonic fields of flow. AU Kozel, K.; Polasek, J.; Vavrincova, M. (Tech. Univ. Prague, Prague, Czechoslovakia) SO Zeitschrift fur Angewandte Mathematik und Mechanik (1980) vol.60, no.7, p.204-6. 6 refs. CODEN: ZAMMAX ISSN: 0044-2267 DT Journal TC Theoretical CY German Democratic Republic LA German AB Applies the relaxation method to the calculation of the two dimensional steady state transonic flow fields during flow round thin profiled cascades and round a thin single profile between two parallel walls. After formulating the differential equations for both instances and stating the difference problems involved, it is shown that the results obtained were in good agreement, in the first instance, with interferograms and, in the second, with experimentally obtained results. L8 ANSWER 290 OF 404 INSPEC COPYRIGHT 1997 IEE AN 81:1613678 INSPEC DN C81000582 TI A product rule ***relaxation*** ***method*** . AU Kirby, R.L. (Computer Sci. Center, Univ. of Maryland, College Park, MD, USA) SO Computer Graphics and Image Processing (June 1980) vol.13, no.2, p.158-89. 11 refs. CODEN: CGIPBG ISSN: 0146-664X DT Journal TC Theoretical CY United States LA English AB Probabilistic relaxation estimates the probabilities of the potential labelings of the nodes of a multigraph. The constraints used are limited to those nodes which are connected by arcs in this multigraph. A multiplicative formula called the product rule is introduced for combining the estimates of several nodes. This formula is then shown to correspond to a discrete relaxation operator. Experiments were made using the product rule to break a substitution cipher and to disambiguate the semantic labeling of the pixels of a color image of a house. The experiments showed that in some applications, the product rule converges more rapidly to estimates that permit making reasonable decisions than did a previous formula using arithmetic averaging. The experiments also suggested ways to refine the relaxation formulas to produce more precise estimates. L8 ANSWER 300 OF 404 INSPEC COPYRIGHT 1997 IEE AN 79:1373449 INSPEC DN C79020046 TI ***Relaxation*** ***methods*** in image processing and analysis. AU Rosenfeld, A. (Computer Sci. Center, Univ. of Maryland, College Park, MD, USA) SO Proceedings of the 4th International Joint Conference on Pattern Recognition Kyoto, Japan: Kyoto, Univ, 1978. p.181-5 of xxii+1166 pp. 12 refs. Conference: Kyoto, Japan, 7-10 Nov 1978 Sponsor(s): Internat. Assoc. Pattern Recognition DT Conference Article TC Theoretical CY Japan LA English AB Describes a class of iterative, parallel processes known as relaxation methods, and reviews some of their uses in image processing and analysis, with emphasis on recent developments. L8 ANSWER 304 OF 404 INSPEC COPYRIGHT 1997 IEE AN 79:1296648 INSPEC DN A79011888 TI The correct use of the dielectric ***relaxation*** ***method*** in studying dimensions, shape, and conformational transitions in proteins. AU Sedykh, N.V.; Fel'dman, Yu.D. (Kazan' Univ., Kazan', USSR) SO Colloid Journal of the USSR (July-Aug. 1977) vol.39, no.4, p.719-20. 13 refs. CODEN: COJOA5 ISSN: 0010-1303 Translation of: Kolloidnyi Zhurnal (July-Aug. 1977) vol.39, no.4, p.806-8. 13 refs. CODEN: KOZHAG ISSN: 0023-2912 DT Journal; Translation Abstracted TC Theoretical CY USSR; United States LA English AB An examination is made of the possibility of correct use of the dipole relaxation method in investigating the shapes, sizes, and confirmation of proteins in solution. Methods are given for taking into account the difficulties associated with problems of macroscopic viscosity, discreteness of the medium, and the selection of a bipolymer model. The sensitivity of the method to change in dimensions of the dipole-active axis of the macromolecule is evaluated. L8 ANSWER 306 OF 404 INSPEC COPYRIGHT 1997 IEE AN 78:1257228 INSPEC DN A78078977; B78046557 TI Coherence ***relaxation*** ***methods*** for holography. AU Leith, E.N. (Univ. of Michigan, Ann Arbor, MI, USA) SO Proceedings of the Society of Photo-Optical Instrumentation Engineers, vol.120. Three-Dimensional Imaging Editor(s): Benton, S.A. Bellingham, WA, USA: Soc. Photo-Optical Instrumentation Engr(s), 1977. p.145-9 of vi+214 pp. 0 refs. Conference: San Diego, CA, USA, 25-26 Aug 1977 Sponsor(s): Soc. Photo-Optical Instrumentation Engr(s) ISBN: 0-89252-147-3 DT Conference Article TC Practical CY United States LA English AB Techniques for producing and receiving holograms in light of reduced coherence are described. Both coherent and incoherent methods are considered. L8 ANSWER 314 OF 404 INSPEC COPYRIGHT 1997 IEE AN 77:1110457 INSPEC DN A77080137 TI ***Relaxation*** ***methods*** for time dependent conservation equations in fluid mechanics. AU Wirz, H.J. (von Karman Inst. for Fluid Dynamics, Rhode-St-Genese, Belgium) SO AGARD Lecture Series No.86 on Computational Fluid Dynamics Neuilly sur Seine, France: AGARD, 1977. p.4/1-49 of v+168 pp. 27 refs. Conference: Rhode-Saint-Genese, Belgium, 19-23 March 1977 Sponsor(s): AGARD DT Conference Article TC Theoretical CY France LA English AB The approximate discrete solution of the fundamental steady state conservation equations of classical physics and in particular fluid mechanics leads in general to large nonlinear systems of algebraic equations, which must be solved iteratively. Of predominant interest is, of course, the reliability of the discrete analogue of the basic conservation laws (numerical model) for finite mesh size. Due to the inherent limitations of available computers (speed, capacity) a second issue plays an equally important role namely the problem of efficiency of iterative methods. The acceleration of the convergence of these methods to solve stationary partial differential equations is the subject of relaxation. L8 ANSWER 317 OF 404 INSPEC COPYRIGHT 1997 IEE AN 77:1048606 INSPEC DN A77039760 TI Gaussian ***relaxation*** ***method*** . I. Homopolar tetrahedral solids. AU Mele, E.J.; Joannopoulos, J.D. (Dept. of Phys., MIT, Cambridge, MA, USA) SO Physical Review B (Solid State) (15 Jan. 1977) vol.15, no.2, p.901-8. 11 refs. CODEN: PLRBAQ ISSN: 0556-2805 DT Journal TC Theoretical CY United States LA English AB A method is developed for extending an empirical tight-binding theory to calculate the densities of state for very large but finite systems. A set of bond-centred analytic wave functions are derived for application of the method to the calculation of charge densities in crystalline Ge as a model homopolar tetrahedral solid. L8 ANSWER 327 OF 404 INSPEC COPYRIGHT 1997 IEE AN 76:878527 INSPEC DN A76027657 TI On Chahine's ***relaxation*** ***method*** for the radiative transfer equation. AU Barcilon, V. (Dept. of Geophys. Sci., Univ. of Chicago, Chicago, IL, USA) SO Journal of the Atmospheric Sciences (Aug. 1975) vol.32, no.8, p.1626-30. 11 refs. CODEN: JAHSAK ISSN: 0022-4928 DT Journal TC Practical; Theoretical CY United States LA English AB The iteration scheme proposed by Chahine for the solution of the radiative transfer equation is discussed in the context of the inverse problem for the thermal structure of the atmosphere. Sufficient conditions which insure the convergence of the iteration are given. L8 ANSWER 328 OF 404 INSPEC COPYRIGHT 1997 IEE AN 76:875651 INSPEC DN A76024138 TI Measurement of the thermal properties of a metal using a ***relaxation*** ***method*** . AU Fox, J.N.; McMaster, R.H. (Dept. of Phys., Indiana Univ. of Pennsylvania, Indiana, PA, USA) SO American Journal of Physics (Dec. 1975) vol.43, no.12, p.1083-6. 7 refs. CODEN: AJPIAS ISSN: 0002-9505 DT Journal TC Experimental CY United States LA English AB A dynamic method for determining the thermal conductivity and specific heat of metals in the range 273 to 373K is described. The necessary theory and experimental techniques for recording the change in temperature as a function of time are given. L8 ANSWER 340 OF 404 INSPEC COPYRIGHT 1997 IEE AN 75:812663 INSPEC DN A75069822 TI Non-linear ***relaxation*** ***methods*** . III. Current-controlled perturbations. AU Rangarajan, S.K. (Materials Sci. Div., Nat. Aeronautical Lab., Bangalore, India) SO Journal of Electroanalytical Chemistry and Interfacial Electrochemistry (25 June 1975) vol.62, no.1, p.31-41. 5 refs. CODEN: JEIEBC ISSN: 0022-0728 DT Journal TC Theoretical CY Switzerland LA English AB For pt.II see ibid., vol.56, no.1, p.27 (1974). A unified theory is presented for the potential perturbations resulting from the disturbance of an electrode electrolyte interface system with an arbitrary current profile. A functional expression, valid for evaluating all orders of potential perturbation when a current of known profile is superimposed, is derived. Generalized expressions for distortion potential and rectification potential are given. The problems of iR drop and charging current compensation are also discussed. => d bib ab 341-343,357,359,361,363,376,377,381,386,389,392,399,404,403,402 L8 ANSWER 341 OF 404 INSPEC COPYRIGHT 1997 IEE AN 75:792706 INSPEC DN A75059938 TI The simulation of skin temperature distributions by means of a ***relaxation*** ***method*** (applied to IR thermography). AU Vermey, G.F. (Dept. of Electrical Engng. Twente Univ. of Technol., Enschede, Netherlands) SO Physics in Medicine and Biology (May 1975) vol.20, no.3, p.384-94. 13 refs. CODEN: PHMBA7 ISSN: 0031-9155 DT Journal TC Theoretical CY United Kingdom LA English AB To solve the differential equation for the heat in a two-layer, rectangular piece of skin tissue, a relaxation method, based on a finite difference technique, is used. The temperature distributions on the skin surface are calculated. The results are used to derive a criterion for the resolution for an infrared thermograph in a specific situation. A major limitation on the resolution in medical thermography is given. As an example of the power of the model, the sensitivity of the temperature profiles for variations of the layer thickness is determined. L8 ANSWER 342 OF 404 INSPEC COPYRIGHT 1997 IEE AN 75:790638 INSPEC DN A75057639 TI ***Relaxation*** ***methods*** in fluid mechanics. AU Lomax, H.; Steger, J.L. (NASA, Moffett Field, CA, USA) SO Annual review of fluid mechanics. Vol.7 Editor(s): Van Dyke, M.; Vincenti, G. Palo Alto, CA, USA: Annual Reviews, 1975. p.63-88 of ix+398 pp. 70 refs. Price: $15.50 ISBN: 0-8243-0707-0 DT Book Article TC Bibliography; General Review CY United States LA English AB It is assumed that the numerical model is an accurate finite-difference representation of the physical problem for which it was constructed. An iterative solution of a coupled set of difference equations is considered and methods are considered that carry successive approximates to a state that is invariant with further iteration and independent of the initial guess. This defines a process of relaxation. The time-like aspect and basic principles of relaxation are presented. L8 ANSWER 343 OF 404 INSPEC COPYRIGHT 1997 IEE AN 75:784468 INSPEC DN C75015687 TI A ***relaxation*** ***method*** for reconstructing objects from noise X-rays. AU Herman, G.T. (State Univ. New York, Buffalo, Amherst, MA, USA) SO Mathematical Programming (Feb. 1975) vol.8, no.1, p.1-19. 22 refs. CODEN: MHPGA4 ISSN: 0025-5610 DT Journal TC Application; Theoretical CY Netherlands LA English AB An algorithm is presented for estimating the density distribution in a cross section of an object from X-ray data which in practice is unavoidably noisy. The data give rise to a large sparse system of inconsistent equations, not untypically 105 equations with 104 unknowns, with only about 1% of the coefficients non-zero. Using the physical interpretation of the equations, each equality can in principle be replaced by a pair of inequalities, giving the limits within which the sum is believed to lie. An algorithm is proposed for solving this set of inequalities. The algorithm is basically a relaxation method. A finite convergence result is proved. In spite of the large size of the system, in the application area of interest practical solution on a computer is possible because of the simple geometry of the problem and the redundancy of equations obtained from nearby X-rays. The algorithm has been implemented, and is demonstrated by actual reconstructions. L8 ANSWER 357 OF 404 INSPEC COPYRIGHT 1997 IEE AN 73:537779 INSPEC DN C73016792 TI A new ***relaxation*** ***method*** for obtaining the lowest eigenvalue and eigenvector of a matrix equation. AU Muda, Y. (Osaka Univ., Suita, Japan) SO International Journal for Numerical Methods in Engineering (1973) vol.6, no.4, p.511-19. 4 refs. CODEN: IJNMBH ISSN: 0029-5981 DT Journal TC Theoretical CY United Kingdom LA English AB The matrix eigenvalue problem Hui= lambda iui is considered. It is shown that when a new approximate vector v(n+1) to u1 (the eigenvector of the lowest eigenvalue) is computed from the present one v(n) by the relation v(n+1)=(1- alpha H+ beta H2)v(n+1)=1- alpha H+BH2- gamma H3)v(n), the convergence rate is at least double that of the gradient method which corresponds to set beta = theta =0. Moreover, by choosing parameters alpha , beta , or gamma properly, one can get about three to five times faster convergence rate than that of the latter method, for H having very small lambda 2- lambda 1 and very large lambda N (the largest eigenvalue). Further modifications are suggested. The relation with the Richardson method is also discussed. L8 ANSWER 359 OF 404 INSPEC COPYRIGHT 1997 IEE AN 73:531350 INSPEC DN A73044722 TI On linear ***relaxation*** ***methods*** . AU Rangarajan, S.K. (Nat. Aeronautical Lab., Bangalore, India) SO Journal of Electroanalytical Chemistry and Interfacial Electrochemistry (9 Feb. 1973) vol.41, no.3, p.459-71. 5 refs. CODEN: JEIEBC ISSN: 0022-0728 DT Journal TC Theoretical CY Switzerland LA English AB A parametric approach towards the classification of relaxation methods is presented. It is emphasised how such a perspective is non-trivial and informative. As a natural consequence, this formal theory of the methodology of linear methods suggests two new current-based transient techniques with two parameters. A comparison of one of these is made with the other methods already available. L8 ANSWER 361 OF 404 INSPEC COPYRIGHT 1997 IEE AN 73:530411 INSPEC DN A73043526 TI Determination of some structure characteristic data of a ribonucleic acid and of a protein through the dielectric ***relaxation*** ***method*** . AU Constantinescu, S.; Dumitrescu, H. (Inst. Politehnic 'Gheorghe Gheorghiu-Dej' Bucuresti, Romania) SO Buletinul Institutului Politehnic 'Gheorghe Gheorghiu-Dej' Bucuresti (Nov.-Dec. 1972) vol.34, no.6, p.29-33. 2 refs. CODEN: BIGBAY ISSN: 0366-0419 DT Journal TC Experimental CY Romania LA Romanian AB The paper shows the results of the study on some bipolymers (a ribonucleic acid and a protein-ovalbumin) through the dielectric relaxation method. Information is obtained concerning the mode of statistical arrangement, the dipole moment, molecular weight, etc. of the studied biopolymers in dilute solutions. L8 ANSWER 363 OF 404 INSPEC COPYRIGHT 1997 IEE AN 73:526795 INSPEC DN C73015129 TI A program using the successive extrapolated ***relaxation*** ***method*** to solve Laplace's equation. AU Kinsner, W.; Torre, E.D. (McMaster Univ., Hamilton, Ont., Canada) SO IEEE Transactions on Microwave Theory and Techniques (May 1973) vol.MTT21, no.5, p.365. 2 refs. CODEN: IETMAB ISSN: 0018-9480 DT Journal TC Application; Theoretical CY United States LA English AB Using Fortran IV, the program determines fields satisfying Laplace's equation with Dirichlet and/or Neumann boundary conditions. Subroutine SER may be applied to other iterative methods. L8 ANSWER 376 OF 404 INSPEC COPYRIGHT 1997 IEE AN 72:374963 INSPEC DN C72009526 TI ***Relaxation*** ***methods*** . AU Birkhoff, G. (Harvard Univ., MA, USA) SO Regional Conference Series in Applied Mathematics (1971) no.1, p.29-37. 10 refs. CODEN: RCSMBO ISSN: 0160-7642 DT Journal TC Theoretical CY United States LA English AB Discusses iterative methods for solving systems of linear (vector) equations of the form Au=b. Methods involving 'relaxation methods' are especially applicable when A is a Stieltjos mat4ix of the form A=D-E-F, F=E/sup T/. The Gauss-Seidal method, Richardson's method, point successive overrelaxation, line and block overrelaxation and rates of convergence of methods are considered. L8 ANSWER 377 OF 404 INSPEC COPYRIGHT 1997 IEE AN 72:374041 INSPEC DN C72008575 TI ***Relaxation*** ***methods*** for pure and mixed integer programming problems. AU Gorry, G.A.; Shapiro, J.F. (MIT, Cambridge, MA, USA); Wolsey, L.A. SO Management Science (Jan. 1971) vol.18, pt.1, no.5, p.229-39. 12 refs. CODEN: MSCIAM ISSN: 0025-1909 DT Journal TC Practical CY United States LA English AB The usefulness of group theoretic methods in solving integer programming (IP) problems is extended by procedures for controlling the size of the groups. The main procedure given shows how an optimal linear programming basis can be altered to reduce the magnitude of its determinant thereby reducing the size of the group induced by the basis. An adaption of Benders' mixed IP algorithm is given which uses these methods. Some limited computational experience is given. L8 ANSWER 381 OF 404 INSPEC COPYRIGHT 1997 IEE AN 71:323191 INSPEC DN C71023758 TI ***Relaxation*** ***method*** for mixed boundary conditions. AU Niki, H.; Kimura, H.; Usui, M.; Akutu, Y. (okayama Coll. Sci., Syuku, Japan) SO Electronics Letters (9 Sept. 1971) vol.7, no.18, p.525-7 CODEN: ELLEAK ISSN: 0013-5194 DT Journal TC Theoretical CY United Kingdom LA English AB The numerical solution of Laplace's equation in 2-dimensional Cartesian co-ordinates with mixed boundary conditions is described using the successive-overrelaxation method for solution with the acceleration parameter decided by a method proposed formerly. Its effectiveness is compared with that of other methods. L8 ANSWER 386 OF 404 INSPEC COPYRIGHT 1997 IEE AN 71:233879 INSPEC DN A71019840 TI A ***relaxation*** ***method*** for the computation of model stellar atmospheres. AU Price, M.J. (Kitt Peak Nat. Obs., Tucson, AZ, USA) SO Theory and observation of normal stellar atmospheres, proceedings of 3rd Harvard-Smithsonian conference on stellar atmospheres Editor(s): Gingerich, O. Cambridge, MA, USA: MIT Press, 1969. p.139-41 of xv+472 pp. Conference: Cambridge, MA, USA, 8-11 April 1968 Sponsor(s): Smithsonian Astrophys. Obs.; Harvard College Obs ISBN: 0-262-07035-9 DT Conference Article TC Theoretical CY United States LA English AB A Monte Carlo relaxation method has been developed for the computation of model stellar atmospheres. The equations of statistical equilibrium for the atomic-level populations are solved simultaneously with the radiative-transfer and electron-temperature equations by use of the constraints of hydrostatic and radiative equilibrium. Selected LTE boundary conditions are applied deep in the atmosphere. In the solution of the statistical-equilibrium equations, all possible electron collisional and radiative processes are considered. In formulating the source function, all atomic processes contributing to the absorption and emission coefficients are considered in microscopic detail. The local electron temperature is obtained by solving the kinetic-energy balance equation for the electron gas. All electron collisional and radiative processes whereby kinetic energy is gained and lost by the electron gas are considered. Thomson scattering is taken into account in formulating the equation of radiative transfer. The free-bound and bound-bound radiation is transferred throughout the atmosphere by use of the Monte Carlo technique. L8 ANSWER 389 OF 404 INSPEC COPYRIGHT 1997 IEE AN 70:187216 INSPEC DN A70068527 TI Thermodynamic properties of interstitial solid solutions by ***relaxation*** ***methods*** . AU Alefeld, G.; Volkl, J.; Tretkowski, J. (Inst. Festkorper, Neutronenphys., Julich, West Germany) SO Journal of the Physics and Chemistry of Solids (Aug. 1970) vol.31, no.8, p.1765-9. 17 refs. CODEN: JPCSAW ISSN: 0022-3697 Conference: International conference on ultrasonic attenuation and internal friction. Providence, RI, USA, 3-6 Sept 1969 Sponsor(s): IUPAP DT Conference Article; Journal CY United Kingdom LA English AB By elastic relaxation methods the derivative ( delta mu / delta rho )T of the chemical potential of solutes can be determined absolutely as a function of temperature and density rho . Therefore useful parameters which characterize the solubility of gases in metals or which determine phase transitions of solutes can be found by elastic relaxation methods. As an example experiments on hydrogen in niobium are discussed. On the basis of experimental parameters (trace of the elastic dipole moment tensor, critical density, critical temperature) it will be argued that the attractive interaction of H in Nb, which is responsible for the phase transition, is of elastic nature. L8 ANSWER 392 OF 404 INSPEC COPYRIGHT 1997 IEE AN 70:125882 INSPEC DN A70029268; C70007947 TI A computer adaptation of southwell's ***relaxation*** ***method*** with application to elastic-plastic stress analysis. AU Wesner, J.W., Jr. CS Carnegie-Mellon Univ., Pittsburgh, PA, USA SO 205 pp. Availability: Univ. Microfilms, Ann Arbor, MI., USA Order no. 68-17620 DT Dissertation CY United States LA English AB Southwell's relaxation method is studied, as a means for solving problems of elastic-perfectly plastic stress analysis with the aid of a digital computer. Procedures are developed for computerized relaxation. A number of the special techniques for facilitating hand relaxation are evaluated, and those which profitably adapt to automatic computation are incorporated into the computerized process. Specific applications of the method to problems of elastic-perfectly plastic stress analysis are considered. Special techniques are developed for the yielded zone. These are then demonstrated by solutions for the notched bar loaded in tension, and for the plane strain indenter. The computer method is evaluated by comparing the notched bar solutions with similar solutions obtained by hand. Results for the indenter are compared with slip-line theory, and with a solution obtained using a finite- element computer code. L8 ANSWER 399 OF 404 INSPEC COPYRIGHT 1997 IEE AN 69:58871 INSPEC DN C69009320 TI A digital computer solution of the Laplace equation using the dynamic ***relaxation*** ***method*** . AU Rushton, K.R.; Laing, L.M. (Univ. Birmingham, UK) SO Aeronautical Quarterly (Nov. 1968) vol.19, pt.4, p.375-87 CODEN: AEQUAY ISSN: 0001-9259 DT Journal CY United Kingdom LA English AB The Dynamic Relaxation solution of the Laplace equation introduces dynamic terms into the basic equation. When this is written as an explicit finite difference formulation it can be solved by an iterative process which only requires a simple substitution routine. The method is easy to programme and requires small storage in the computer. By studying problems involving wind tunnel interference in steady flow, the potentialities of the method are demonstrated. L8 ANSWER 404 OF 404 INSPEC COPYRIGHT 1997 IEE AN 69:6426 INSPEC DN A69004293 TI A systematic ***relaxation*** ***method*** for the determination of the normal modes and the natural frequencies of vibrating systems. AU Allman, D.J.; Brotton, D.M. (Dept. Civil Engineering, StrEngineering Div., Univ. Manchester Inst. Sci. Technology, UK) SO International Journal of Mechanical Sciences (Feb. 1968) vol.10, no.2, p.129-41. 10 refs. CODEN: IMSCAW ISSN: 0020-7403 DT Journal CY United Kingdom LA English AB A systematic relaxation method for the determination of the normal modes and natural frequencies of harmonic and quasi-harmonic vibrating systems is presented. The method is capable of dealing with systems which can be idealized as discrete masses with interconnecting massless elastic springs. The method is based on the numerical integration of the restraint accelerations acting on the masses of a system as it vibrates in a constrained configuration and it is thus convenient for use with a digital comowever,Hsolutions to systems with a small number of degrees of freedom may be obtained by hand calculations alone. L8 ANSWER 403 OF 404 INSPEC COPYRIGHT 1997 IEE AN 69:19149 INSPEC DN C69002847 TI Numerical solution of the problem of heat propagation in one dimension by the iterative super- ***relaxation*** ***method*** . AU Ribero dos Santos, J.; Rigal, A. SO Remote Sensing of Environment (July 1968) vol.2, no.10, p.53-64 CODEN: RSEEA7 ISSN: 0034-4257 DT Journal CY United States LA French AB Concerns the problem of heat propagation or diffusion in one dimension in an isotropic homogeneous medium. The 2nd order approximation of the problem can be expressed in a formula depending on a parameter theta . For a certain value of theta a 4th order approximation in x and a second order approximation in t can be obtained. The problem is solved by the iterative super-relaxation method, applying the property of the reducibility of the total linear system. A numerical example is also given. L8 ANSWER 402 OF 404 INSPEC COPYRIGHT 1997 IEE AN 69:19158 INSPEC DN C69002856 TI On the use of gradient ***relaxation*** ***method*** for solution of a system of nonlinear equations. AU Spiridonov, V.S. SO Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki (July 1968) vol.8, no.4, p.872-3 CODEN: ZVMFAN ISSN: 0044-4669 DT Journal CY USSR LA Russian AB An algorithm is given for convergence of an iterative trajectory-following method if the vicinity of a root is convex. =>