Computation of Plain Unitary Rotations Transforming a General Matrix to Triangular Form

Previous article Next article Computation of Plain Unitary Rotations Transforming a General Matrix to Triangular FormWallace GivensWallace Givenshttps://doi.org/10.1137/0106004PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 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, available from Office of Technical Services, Washington 25, D. C. MR0063771 0055.35005 CrossrefGoogle Scholar2 Wallace Givens, The characteristic value-vector problem, J. Assoc. Comput. Mach., 4 (1957), 298–307 MR0092224 CrossrefISIGoogle Scholar3 E. G. Kogbetliantz, Solution of linear equations by diagonalization of coefficient matrix, Quart. Appl. Math., 13 (1955), 123–132 MR0088795 0066.10101 CrossrefGoogle Scholar4 Mark Lotkin, Characteristic values of arbitrary matrices, Quart. Appl. Math., 14 (1956), 267–275 MR0090576 0073.33804 CrossrefGoogle Scholar5 J. H. Wilkinson, The calculation of the latent roots and vectors of matrices on the pilot model of the A.C.E, Proc. Cambridge Philos. Soc., 50 (1954), 536–566, The use of iterative methods for finding the latent roots and vectors of matrices, Math. Tables Aids Comput., 9 (1955), pp. 184–191. MR0063775 0056.12202 CrossrefISIGoogle Scholar6 William Feller and , George E. Forsythe, New matrix transformations for obtaining characteristic vectors, Quart. Appl. Math., 8 (1951), 325–331 MR0039373 0043.01502 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Necessary and Sufficient Conditions for the Existence of Positive Definite Solutions to the Symmetric Recursive Inverse Eigenvalue Problem31 July 2006 | SIAM Journal on Matrix Analysis and Applications, Vol. 26, No. 4AbstractPDF (223 KB)Parallel Processing in the Adaptive Control of Linear Systems17 July 2006 | SIAM Journal on Matrix Analysis and Applications, Vol. 9, No. 1AbstractPDF (933 KB)Numerical Methods for Large Sparse Linear Least Squares Problems14 July 2006 | SIAM Journal on Scientific and Statistical Computing, Vol. 5, No. 3AbstractPDF (2012 KB)Some Efficient Algorithms for Solving Systems of Nonlinear Equations14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 10, No. 2AbstractPDF (1603 KB)Modern Error Analysis18 July 2006 | SIAM Review, Vol. 13, No. 4AbstractPDF (2275 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)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)Computing Eigenvalues of Non-Hermitian Matrices by Methods of Jacobi TypeRobert L. Causey10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 6, No. 2AbstractPDF (939 KB) Volume 6, Issue 1| 1958Journal of the Society for Industrial and Applied Mathematics History Submitted:22 November 1957Published online:28 July 2006 InformationCopyright © 1958 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0106004Article page range:pp. 26-50ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics