On Cyclic Jacobi Methods
Eldon R. Hansen · Journal of the Society for Industrial and Applied Mathematics · 1963
Previous article Next article On Cyclic Jacobi MethodsEldon R. HansenEldon R. Hansenhttps://doi.org/10.1137/0111032PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] 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[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] 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[4] C. G. J. Jacobi, über ein leichtes Varfahren, die in der Theorie der Säkularstörungen vorkommenden Gleichungen numerisch aufzulösen, J. Reine Angew. Math., 30 (1846), 51–95 CrossrefGoogle Scholar[5] David A. Pope and , C. Tompkins, Maximizing functions of rotations. Experiments concerning speed of diagonalization of symmetric matrices using Jacobi's method, J. Assoc. Comput. Mach., 4 (1957), 459–466 MR0096355 CrossrefISIGoogle Scholar[6] Rand Corp., A million random digits with 100,000 normal deviates, The Free Press, Glencoe, Ill., 1955xxv+200 MR0067568 Google Scholar[7] Eldon R. Hansen, On quasicyclic Jacobi methods, J. Assoc. Comput. Mach., 9 (1962), 118–135 MR0134464 0121.11303 CrossrefISIGoogle Scholar[8] Eldon R. Hansen, Ph.D. Thesis, On Jacobi methods and block-Jacobi methods for computing matrix eigenvalues, Stanford University, 1960, July Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A Hierarchically Blocked Jacobi SVD Algorithm for Single and Multiple Graphics Processing Units20 January 2015 | SIAM Journal on Scientific Computing, Vol. 37, No. 1AbstractPDF (538 KB)A Global Convergence Proof for Cyclic Jacobi Methods with Block Rotations13 November 2009 | SIAM Journal on Matrix Analysis and Applications, Vol. 31, No. 3AbstractPDF (395 KB)Convergence of a Block‐Oriented Quasi‐Cyclic Jacobi Method19 March 2007 | SIAM Journal on Matrix Analysis and Applications, Vol. 29, No. 2AbstractPDF (247 KB)On the Parallel Implementation of Jacobi and Kogbetliantz Algorithms13 July 2006 | SIAM Journal on Scientific Computing, Vol. 15, No. 6AbstractPDF (1882 KB)On the Convergence of the Cyclic Jacobi Method for Parallel Block Orderings17 July 2006 | SIAM Journal on Matrix Analysis and Applications, Vol. 10, No. 3AbstractPDF (2343 KB)The Solution of Singular-Value and Symmetric Eigenvalue Problems on Multiprocessor Arrays31 July 2006 | SIAM Journal on Scientific and Statistical Computing, Vol. 6, No. 1AbstractPDF (1589 KB)Today’s Computational Methods of Linear Algebra18 July 2006 | SIAM Review, Vol. 9, No. 3AbstractPDF (3431 KB) Volume 11, Issue 2| 1963Journal of the Society for Industrial and Applied Mathematics History Submitted:12 June 1961Published online:13 July 2006 InformationCopyright © 1963 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0111032Article page range:pp. 448-459ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics