A Survey of Some Closed Methods for Inverting Matrices
A. S. Householder · Journal of the Society for Industrial and Applied Mathematics · 1957
Previous article A Survey of Some Closed Methods for Inverting MatricesAlston S. HouseholderAlston S. Householderhttps://doi.org/10.1137/0105011PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. Bodewig, Zum Matrizenkalkul, Nederl. Akad. Wetensch. Proc. Ser. A. 58 = Indagationes Math., 17 (1955), 95–106; corrigenda, 260 MR0072837 0067.25303 Google Scholar[2] E. Bodewig, Matrix calculus, North-Holland Publishing Company, Amsterdam, 1956xii+334 MR0080363 Google Scholar[3] Edward J. Craig, The N-step iteration procedures, J. Math. Phys., 34 (1955), 64–73 MR0070260 0065.10901 CrossrefGoogle Scholar[4] George E. Forsythe, Solving linear algebraic equations can be interesting, Bull. Amer. Math. Soc., 59 (1953), 299–329 MR0056372 0050.34603 CrossrefISIGoogle Scholar[5] J. Guest, The solution of linear simultaneous equations by matrix iteration, Austral. J. Phys., 8 (1955), 425–439 MR0076434 0068.32102 CrossrefGoogle Scholar[6] Alston S. Householder, Principles of numerical analysis, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953x+274 MR0059056 0051.34602 Google Scholar[7] Alston S. Householder, Bibliography on numerical analysis, J. Assoc. Comput. Mach., 3 (1956), 85–100 MR0077214 CrossrefISIGoogle Scholar[8] Alston S. Householder, Terminating and nonterminating iterations for solving linear systems, J. Soc. Indust. Appl. Math., 3 (1955), 67–72 10.1137/0103005 MR0074093 0067.35501 LinkISIGoogle Scholar[9] Gabriel Kron, Improved procedure for interconnecting piece-wise solutions, J. Franklin Inst., 262 (1956), 385–392 10.1016/0016-0032(56)90079-5 MR0085601 CrossrefGoogle Scholar[10] Petar Madić, Sur une méthode de résolution des systèmes d'équations algébriques linéaires, C. R. Acad. Sci. Paris, 242 (1956), 439–441 MR0074916 Google Scholar[11] Manuel Peres, Sôbre a resolução dos sistemas de equações lineares simultanes, Las Ciencias, Madrid, 17 (1952), 443–449 Google Scholar[12] J. Paul Roth, An algebraic topological approach to Kron's method, ECP Tech. Report, 56-03, I. Inst. Adv. Study, 1956 Google Scholar[13] Richard, R. Sabroff, Masters Thesis, A critical study of Kron's method of “tearing” (i.e. “Diakoptics”), M. S. Thesis, Univ. of Wisconsin, 1956 Google Scholar[14] J. Sherman and , W. J. Morrison, Adjustment of an inverse matrix corresponding to changes in the elements of a given column or a given row of the original matrix, Ann. Math. Statistics, 20 (1949), 621– 0037.00901 ISIGoogle Scholar[15] Max A. Woodbury, Inverting modified matrices, Statistical Research Group, Memo. Rep. no. 42, Princeton University, Princeton, N. J., 1950, 4– MR0038136 Google Scholar Previous article FiguresRelatedReferencesCited byDetails Inversion of Covariance Matrices: Explicit FormulaeCzesław Ste¸pniak17 July 2006 | SIAM Journal on Matrix Analysis and Applications, Vol. 12, No. 3AbstractPDF (261 KB)Solution of Modified Matrix EquationsStephen B. Haley14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 24, No. 4AbstractPDF (601 KB)On Deriving the Inverse of a Sum of MatricesH. V. Henderson and S. R. Searle17 February 2012 | SIAM Review, Vol. 23, No. 1AbstractPDF (970 KB)A Class of Methods for Inverting MatricesAlston S. Householder10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 6, No. 2AbstractPDF (536 KB) Volume 5, Issue 3| 1957Journal of the Society for Industrial and Applied Mathematics History Submitted:24 May 1957Published online:10 July 2006 InformationCopyright © 1957 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0105011Article page range:pp. 155-169ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics