Simultaneous, Successive and Alternating Direction Iteration Schemes (1960)

Previous article Next article Simultaneous, Successive and Alternating Direction Iteration SchemesJ. HellerJ. Hellerhttps://doi.org/10.1137/0108009PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. Householder, Notes on numerical analysis, University of Michigan, 1957 Google Scholar[2] R. Courant, Variational methods for the solution of problems of equilibrium and vibrations, Bull. Amer. Math. Soc., 49 (1943), 1–23 MR0007838 0063.00985 CrossrefGoogle Scholar[3] Lothar Collatz, Numerische Behandlung von Differentialgleichungen, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete. Band LX, Springer-Verlag, Berlin, Göttingen, Heidelberg, 1951xiii+458 MR0043563 0044.33103 CrossrefGoogle Scholar[4] H. B. Keller, On some iterative methods for solving elliptic difference equations, AEC Research and Development Report NYO-7971, New York University, 1957 Google Scholar[5] P. Rózsa, A matrix-számitás alkalmazáso rudak és lemezek sztatihájdban, Magyar Tud. Akad. Budapest, 1 (1956), 593–621 Google Scholar[6] E. Windsor, Masters Thesis, Interactive solutions of biharmonic difference equations, Master's thesis, New York University, 1957 Google Scholar[7] David Young, Iterative methods for solving partial difference equations of elliptic type, Trans. Amer. Math. Soc., 76 (1954), 92–111 MR0059635 0055.35704 CrossrefISIGoogle Scholar[8] R. J. Arms, , L. D. Gates and , B. Zondek, A method of block iteration, J. Soc. Indust. Appl. Math., 4 (1956), 220–229 10.1137/0104012 MR0119405 0077.32502 LinkISIGoogle Scholar[8A] B. Friedman, The iterative solution of elliptic difference equations, Research and Development Report NYO-7698, AEC, New York University, 1957 Google Scholar[9] J. Heller, Ordering properties of linear successive iteration schemes applied to multi-diagonal type linear systems, J. Soc. Indust. Appl. Math., 5 (1957), 238–243 10.1137/0105016 MR0092217 0115.34201 LinkISIGoogle Scholar[10] C. C. MacDuffee, The Theory of Matrices, Chelsea, New York, 1946 Google Scholar[11] G. Birkiioff and , R. S. Varga, Implicit alternating direction methods, Report WAPD-T-650, Westing house Electric Corporation, Pittsburgh, 1957 Google Scholar[12] Donald A. Flanders and , George Shortley, Numerical determination of fundamental modes, J. Appl. Phys., 21 (1950), 1326–1332 10.1063/1.1699598 MR0040075 0039.34101 CrossrefISIGoogle Scholar[13] D. W. Peaceman and , H. H. Rachford, Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. Appl. Math., 3 (1955), 28–41 10.1137/0103003 MR0071874 0067.35801 LinkISIGoogle Scholar[14] Jim Douglas, Jr. and , H. H. Rachford, Jr., On the numerical solution of heat conduction problems in two and three space variables, Trans. Amer. Math. Soc., 82 (1956), 421–439 MR0084194 0070.35401 CrossrefGoogle Scholar[15] S. D. Conte and , R. T. Dames, An alternating direction method for solving the biharmonic equation., Math. Tables Aids Comput., 12 (1958), 198–205 MR0105813 0083.12304 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Tensor Product Analysis of Alternating Direction Implicit MethodsRobert E. Lynch, John R. Rice, and Donald H. Thomas13 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 13, No. 4AbstractPDF (1100 KB)Numerical Solution of Plane Elasticity ProblemsD. S. Griffin and R. S. Varga13 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 4AbstractPDF (1358 KB) Volume 8, Issue 1| 1960Journal of the Society for Industrial and Applied Mathematics History Submitted:03 February 1959Accepted:03 June 1959Published online:10 July 2006 InformationCopyright © 1960 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0108009Article page range:pp. 150-173ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics