Computing Eigenvalues of Non-Hermitian Matrices by Methods of Jacobi Type

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Previous article Next article Computing Eigenvalues of Non-Hermitian Matrices by Methods of Jacobi TypeRobert L. CauseyRobert L. Causeyhttps://doi.org/10.1137/0106010PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] C. G. J. Jacobi, Ein leichtes Verfahren, die in der Theorie der Säkularstörungen vorkommenden Gleichungen numerisch aufzulösen, J. Reine Angew. Math., 30 (1846), 51–95 030.0852cj CrossrefGoogle Scholar[2] Robert T. Gregory, Computing eigenvalues and eigenvectors of a symmetric matrix on the ILLIAC, Math. Tables and Other Aids to Computation, 7 (1953), 215–220 MR0057643 0052.35703 CrossrefGoogle Scholar[3] J. Greenstadt, A method for finding roots of arbitrary matrices, Math. Tables Aids Comput., 9 (1955), 47–52 MR0073283 0065.24801 CrossrefGoogle Scholar[4] Mark Lotkin, Characteristic values of arbitrary matrices, Quart. Appl. Math., 14 (1956), 267–275 MR0090576 0073.33804 CrossrefGoogle Scholar[5] E. Bodewig, Matrix calculus, North-Holland Publishing Company, Amsterdam, 1956xii+334 MR0080363 0086.32501 Google 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] G. E. Forsythe and , P. Henrici, The cyclic Jacobi method for computing the principal values of a complex matrix, Trans. Amer. Math. Soc., 94 (1960), 1–23 MR0109825 0092.32504 CrossrefGoogle Scholar[8] Peter Henrici, On the speed of convergence of cyclic and quasicyclic Jacobi methods for computing eigenvalues of Hermitian matrices, J. Soc. Indust. Appl. Math., 6 (1958), 144–162 10.1137/0106008 MR0095582 0097.32601 LinkISIGoogle Scholar[9] Wallace Givens, Numerical conputation of the characteristic values of a real symmetric matrix, Rep. ORNL 1574, Oak Ridge National Laboratory, Oak Ridge, Tenn., 1954vi+107 MR0063771 0055.35005 CrossrefGoogle Scholar[10] H. H. Goldstine, multilith typescript, Institute for Advanced Study. Google Scholar[11] C. C. MacDuffee, The Theory of Matrices, Chelsea, New York, 1946 Google Scholar[12] Wallace Givens, The characteristic value-vector problem, J. Assoc. Comput. Mach., 4 (1957), 298–307 MR0092224 CrossrefISIGoogle Scholar[13] Wallace Givens, Computation of plane unitary rotations transforming a general matrix to triangular form, J. Soc. Indust. Appl. Math., 6 (1958), 26–50 10.1137/0106004 MR0092223 0087.11902 LinkISIGoogle Scholar[14] Elmer E. Osborne, On acceleration and matrix deflation processes used with the power method, J. Soc. Indust. Appl. Math., 6 (1958), 279–287 10.1137/0106019 MR0096354 0086.11001 LinkISIGoogle Scholar[15] J. B. Rosser, , C. Lanczos, , M. R. Hestenes and , W. Karush, Separation of close eigenvalues of a real symmetric matrix, J. Research Nat. Bur. Standards, 47 (1951), 291–297 MR0048914 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On Asymptotic Convergence of Nonsymmetric Jacobi Algorithms19 March 2008 | SIAM Journal on Matrix Analysis and Applications, Vol. 30, No. 1AbstractPDF (239 KB)On the Generalized Schur Decomposition of a Matrix Pencil for Parallel Computation13 July 2006 | SIAM Journal on Scientific and Statistical Computing, Vol. 12, No. 4AbstractPDF (2511 KB)A Jacobi-Type Method for Triangularizing an Arbitrary Matrix14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 12, No. 4AbstractPDF (421 KB)A Jacobi-Like Method for the Automatic Computation of Eigenvalues and Eigenvectors of an Arbitrary Matrix13 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 10, No. 1AbstractPDF (946 KB)Computing Eigenvalues of Complex Matrices by Determinant Evaluation and by Methods of Danilewski and WielandtWerner L. Frank10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 6, No. 4AbstractPDF (1300 KB)The Computation of Eigenvalues and Eigenvectors of a MatrixPaul A. White10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 6, No. 4AbstractPDF (4289 KB)On the Speed of Convergence of Cyclic and Quasicyclic Jacobi Methods for Computing Eigenvalues of Hermitian MatricesPeter Henrici10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 6, No. 2AbstractPDF (1475 KB) Volume 6, Issue 2| 1958Journal of the Society for Industrial and Applied Mathematics History Submitted:04 February 1958Published online:10 July 2006 InformationCopyright © 1958 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0106010Article page range:pp. 172-181ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics