Optimum Alternating-Direction-Implicit Iteration Parameters for a Model Problem
1962; Society for Industrial and Applied Mathematics; Volume: 10; Issue: 2 Linguagem: Inglês
10.1137/0110025
ISSN2168-3484
Autores Tópico(s)Mathematical Inequalities and Applications
ResumoPrevious article Next article Optimum Alternating-Direction-Implicit Iteration Parameters for a Model ProblemE. L. WachspressE. L. Wachspresshttps://doi.org/10.1137/0110025PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. L. Wachspress and , G. J. Habetler, An alternating-direction-implicit iteration technique, J. Soc. Indust. Appl. Math., 8 (1960), 403–424 10.1137/0108027 MR0114308 0158.33901 LinkISIGoogle Scholar[2] N. I. Achieser, Theory of approximation, Translated by Charles J. Hyman, Frederick Ungar Publishing Co., New York, 1956x+307, (from Russian), Chapter III MR0095369 0072.28403 Google Scholar[3] R. M. Thrall and , L. Tornheim, Vector Spaces and Matrices, Wiley, New York, 1957, 189– 0077.02002 Google Scholar[4] B. L. van der Waerden, Modern Algebra. Vol. I, Frederick Ungar Publishing Co., New York, N. Y., 1949, 56– MR0029363 0039.00902 Google Scholar[5] G. H. Hardy, , A. E. Littlewood and , G. Polya, Inequalities, Cambridge Univ. Press, London, 1934, Chapter II 0010.10703 Google Scholar[6] Th. Motzkin, Approximation by curves of a unisolvent family, Bull. Amer. Math. Soc., 55 (1949), 789–793 MR0031111 0034.33302 CrossrefISIGoogle Scholar[7] Leonard Tornheim, On n-parameter families of functions and associated convex functions, Trans. Amer. Math. Soc., 69 (1950), 457–467 MR0038383 0040.02901 ISIGoogle Scholar[8] John R. Rice, The characterization of best nonlinear Tchebycheff approximations, Trans. Amer. Math. Soc., 96 (1960), 322–340 MR0117490 0146.08204 CrossrefGoogle Scholar[9] Carl de Boor and , John R. Rice, Chebyshev approximation by $a\Pi {x-r\sb{i}\over x+s\sb{i}}$ and application to ADI iteration, J. Soc. Indust. Appl. Math., 11 (1963), 159–169, personal communication from the authors. 10.1137/0111012 MR0161461 0116.04503 LinkISIGoogle Scholar[10] E. G. D'yakonov, An iteration method for solving systems of finite difference equations, Soviet Mathematics (AMS Translation), 2 (1961), 647–, May 0102.11605 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Isogeometric Preconditioners Based on Fast Solvers for the Sylvester EquationSIAM Journal on Scientific Computing, Vol. 38, No. 6 | 15 November 2016AbstractPDF (692 KB)Low-Rank Solution of Lyapunov EquationsSIAM Review, Vol. 46, No. 4 | 4 August 2006AbstractPDF (637 KB)Low Rank Solution of Lyapunov EquationsSIAM Journal on Matrix Analysis and Applications, Vol. 24, No. 1 | 31 July 2006AbstractPDF (258 KB)Application of ADI Iterative Methods to the Restoration of Noisy ImagesSIAM Journal on Matrix Analysis and Applications, Vol. 17, No. 1 | 17 February 2012AbstractPDF (2458 KB)Periodicity Effects on the Iterative Solution of Elliptic Difference EquationsSIAM Journal on Numerical Analysis, Vol. 8, No. 2 | 14 July 2006AbstractPDF (1789 KB)Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics (Eugene L. Wachspress)SIAM Review, Vol. 9, No. 4 | 18 July 2006AbstractPDF (441 KB)Tensor Product Analysis of Alternating Direction Implicit MethodsJournal of the Society for Industrial and Applied Mathematics, Vol. 13, No. 4 | 13 July 2006AbstractPDF (1100 KB)Extended Application of Alternating Direction Implicit Iteration Model Problem TheoryJournal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 4 | 13 July 2006AbstractPDF (1573 KB)Chebyshev Approximation by $a\Pi \frac{{x - r_i }}{{x + s_i }}$ and Application to ADI IterationCarl de Boor and John R. RiceJournal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 1 | 13 July 2006AbstractPDF (838 KB) Volume 10, Issue 2| 1962Journal of the Society for Industrial and Applied Mathematics229-393 History Submitted:05 July 1961Accepted:27 December 1961Published online:13 July 2006 InformationCopyright © 1962 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0110025Article page range:pp. 339-350ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics
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