Tensor Product Analysis of Alternating Direction Implicit Methods

Previous article Next article Tensor Product Analysis of Alternating Direction Implicit MethodsRobert E. Lynch, John R. Rice, and Donald H. ThomasRobert E. Lynch, John R. Rice, and Donald H. Thomashttps://doi.org/10.1137/0113067PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Louis Auslander and , Robert E. MacKenzie, Introduction to differentiable manifolds, McGraw-Hill Book Co., Inc., New York, 1963ix + 219 MR0161254 0184.24905 Google Scholar[2] Garrett Birkhoff and , Richard S. Varga, Implicit alternating direction methods, Trans. Amer. Math. Soc., 92 (1959), 13–24 MR0105814 0093.31201 CrossrefGoogle Scholar[3] G. Birkhoff, , R. S. Varga and , D. Young, Alternating direction implicit methods, Advances in Computers, 3 (1962), 189–273 0111.31402 CrossrefGoogle Scholar[4] Carl de Boor and , John R. Rice, Chebyshev approximation by aΠ x-ri x+si and application to ADI iteration, J. Soc. Indust. Appl. Math., 11 (1963), 159–169 10.1137/0111012 MR0161461 0116.04503 LinkISIGoogle Scholar[5] Carl de Boor and , John R. Rice, Tensor products and commutative matrices, J. Soc. Indust. Appl. Math., 12 (1964), 892–896 10.1137/0112077 MR0175921 0156.26802 LinkISIGoogle Scholar[6] N. Bourbaki, Éléments de mathématique. VII. Première partie: Les structures fondamentales de l'analyse. Livre II: Algèbre. Chapitre III: Algèbre multilinéaire, Actualités Sci. Ind., no. 1044, Hermann et Cie., Paris, 1948ii+157+ii MR0026989 0039.25902 Google Scholar[7] A. A. Samarskii˘ and , V. B. Andreev, A difference scheme of higher accuracy for an equation of elliptic type in several space variables, Ž. Vyčisl. Mat. i Mat. Fiz., 3 (1963), 1006–1013 MR0158558 Google Scholar[8] Richard S. Varga, Matrix iterative analysis, Prentice-Hall Inc., Englewood Cliffs, N.J., 1962xiii+322 MR0158502 0133.08602 Google Scholar[9] Paul R. Halmos, Finite-dimensional vector spaces, The University Series in Undergraduate Mathematics, D. Van Nostrand Co., Inc., Princeton-Toronto-New York-London, 1958viii+200, 2nd ed. MR0089819 0107.01404 Google Scholar[10] Nathan Jacobson, Lectures in abstract algebra. Vol. II. Linear algebra, D. Van Nostrand Co., Inc., Toronto-New York-London, 1953xii+280 MR0053905 0053.21204 CrossrefGoogle Scholar[11] R. E. Lynch, , J. R. Rice and , D. H. Thomas, Tensor product analysis of partial difference equations, Bull. Amer. Math. Soc., 70 (1964), 378–384 MR0169390 0126.12704 CrossrefISIGoogle Scholar[12] William Edmund Milne, Numerical solution of differential equations, John Wiley & Sons Inc., New York, 1953xii+275 MR0068321 0050.12202 Google Scholar[13] Marvin Marcus, Basic theorems in matrix theory, Nat. Bur. Standards Appl. Math. Ser., 57 (1960), iv+27 MR0109824 0086.32502 Google Scholar[14] J. Heller, Simultaneous, successive and alternating direction iteration schemes, J. Soc. Indust. Appl. Math., 8 (1960), 150–173 10.1137/0108009 MR0121978 0109.34602 LinkISIGoogle Scholar[15] E. L. Wachspress, Optimum alternating-direction-implicit iteration parameters for a model problem, J. Soc. Indust. Appl. Math., 10 (1962), 339–350 10.1137/0110025 MR0150935 0111.31401 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails ADI Methods for Cubic Spline Collocation Discretizations of Elliptic PDEP. Tsompanopoulou and E. Vavalis25 July 2006 | SIAM Journal on Scientific Computing, Vol. 19, No. 2AbstractPDF (824 KB)Tensor Product Generalized ADI Methods for Separable Elliptic Problems14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 24, No. 1AbstractPDF (1728 KB) Volume 13, Issue 4| 1965Journal of the Society for Industrial and Applied Mathematics History Submitted:28 February 1964Accepted:19 April 1965Published online:13 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113067Article page range:pp. 995-1006ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics