Fernando's solution to Wilkinson's problem: An application of double factorization
type: Item
instance of: scholarly article
title: Fernando's solution to Wilkinson's problem: An application of double factorization
zbMATH Open document ID: 0886.65033
DOI: 10.1016/S0024-3795(97)80053-5
author: Beresford N. Parlett
author: Inderjit S. Dhillon
published in: Linear Algebra and its Applications
publication date: 1998-04-13T00:00:00Z
review text: An algorithm for the computation of eigenvectors to a real symmetric tridiagonal matrix, when eigenvalues are already computed, is studied. It is built up on a recursion, used already by \textit{W. Givens} (J. Assoc. Comput. Mach. 4, 298-307 (1957; MR 19.10806). Following a suggestion by \textit{K. V. Fernando} [On computing an eigenvector of a tridiagonal matrix. I: Basic results, SIAM J. Matrix Anal. Appl. 18, No. 4, 1013-1034 (1997)], it is shown at which coordinate this recursion should be started, in order to be stable and yield orthogonal eigenvectors, also when the eigenvalue approximations are multiple to the accuracy used. These starting coordinates are found by running Gaussian elimination both forwards and backwards. Several numerical examples are included.
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 1089500
zbMATH Keywords: double factorization
zbMATH Keywords: algorithm
zbMATH Keywords: eigenvalues
zbMATH Keywords: Gaussian elimination
zbMATH Keywords: numerical examples
zbMATH Keywords: eigenvectors
zbMATH Keywords: symmetric tridiagonal matrix
reviewed by: Axel Ruhe
describes a project that uses: LAPACK
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1089500