Partitioning and Tearing Systems of Equations

Previous article Partitioning and Tearing Systems of EquationsDonald V. StewardDonald V. Stewardhttps://doi.org/10.1137/0702028PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 G. Kron, Diakoptics, Macdonald, London, 1963 Google Scholar2 L. R. Klein and , A. S. Goldberger, An Econometric Model of the United States 1929–1952, North-Holland, Amsterdam, 1955 Google Scholar3 H. F. Bückner, Remarks on the method of tearing, unpublished Google Scholar4 G. L. Nemhauser and , D. J. Wilde, Strategies for optimizing macrosystems, presented to the American Institute of Chemical Engineers, Las Vegas, 1964, September 26 Google Scholar5 D. F. Rudd and , D. V. Steward, On information flow and process design calculations, presented to the American Institute of Chemical Engineers, Las Vegas, 1964, September 26 Google Scholar6 L. Klein and , G. Fromm, The SSRC-Brookings quarterly econometric model of the United States: model properties, presented at the Annual Meeting of Allied Social Science Association, Chicago, 1964, December 26-30 Google Scholar7 Donald V. Steward, On an approach to techniques for the analysis of the structure of large systems of equations, SIAM Rev., 4 (1962), 321–342 10.1137/1004088 MR0145652 0112.34602 LinkISIGoogle Scholar8 R. W. H. Sargent and , A. W. Westerberg, Speed-up in chemical engineering design, Trans. Instn. Chem. Engrs., 42 (1964), T190–T197 Google Scholar9 C. C. Holt, , R. Shirey, , D. Steward, , J. L. Midler and , A. H. Stroud, Program SIMULATE, A User's and Programmer's Manual, Social Systems Research Institute, University of Wisconsin, Madison, 1964 Google Scholar10 Frank Harary, A graph theoretic approach to matrix inversion by partitioning, Numer. Math., 4 (1962), 128–135 10.1007/BF01386304 MR0139545 0109.09003 CrossrefGoogle Scholar11 Frank Harary, A graph theoretic method for the complete reduction of a matrix with a view toward finding its eigenvalues, J. Math. Phys., 38 (1959/1960), 104–111 MR0109793 0087.01701 CrossrefGoogle Scholar12 A. L. Dulmage and , N. S. Mendelsohn, On the inversion of sparse matrices, Math. Comp., 16 (1962), 494–496 MR0156452 0115.11301 CrossrefGoogle Scholar13 C. S. Lorens, Flowgraphs: For the Modeling and Analysis of Linear Systems, McGraw-Hill, New York, 1964 Google Scholar14 S. Parter, The use of linear graphs in Gauss elimination, SIAM Rev., 3 (1961), 119–130 10.1137/1003021 MR0143349 0102.11302 LinkISIGoogle Scholar15 Hans F. Bückner, Numerical methods for integral calculationsSurvey of numerical analysis, McGraw-Hill, New York, 1962, 439–467 MR0135733 Google Scholar16 Hans F. Bückner, Elektronische rechenmaschinen in der Starkstromtechnik, Anwendung elektrischer Rechenanlagen in der Starkstromtechnik, VDE-Verlag GMBH, Berlin, 1958 Google Scholar17 Alston S. Householder, Principles of numerical analysis, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953x+274 MR0059056 0051.34602 Google Scholar18 R. A. Frazer, , W. J. Duncan and , A. R. Collar, Elementary Matrices, Cambridge University Press, Cambridge, 1953, 20– Google Scholar Previous article FiguresRelatedReferencesCited byDetails Updating the Inverse of a MatrixWilliam W. Hager17 February 2012 | SIAM Review, Vol. 31, No. 2AbstractPDF (2126 KB)Theory of Output Set Assignments and Degree Switching OperationsBharat Kinariwala and Kabekode V. S. Bhat13 July 2006 | SIAM Journal on Computing, Vol. 5, No. 4AbstractPDF (1422 KB)Computations with Sparse MatricesR. P. Tewarson18 July 2006 | SIAM Review, Vol. 12, No. 4AbstractPDF (1825 KB)The Product Form of Inverses of Sparse Matrices and Graph TheoryR. P. Tewarson18 July 2006 | SIAM Review, Vol. 9, No. 1AbstractPDF (962 KB) Volume 2, Issue 2| 1965Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis History Submitted:21 January 1965Published online:14 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0702028Article page range:pp. 345-365ISSN (print):0887-459XISSN (online):2168-3581Publisher:Society for Industrial and Applied Mathematics