Relatively robust representations of symmetric tridiagonals
type: Item
instance of: scholarly article
title: Relatively robust representations of symmetric tridiagonals
zbMATH Open document ID: 0948.65026
DOI: 10.1016/S0024-3795(99)00262-1
published in: Linear Algebra and its Applications
publication date: 2000-11-22T00:00:00Z
review text: The triangular factorization of an unreduced symmetric tridiagonal matrix is considered with respect to relative changes in the nontrivial entries of the lower left matrix and the diagonal part. The effect of these changes is modeled by diagonal scaling matrices. Relative changes in the eigenvalues of the tridiagonal matrix are studied in detail with respect to the inner perturbations induced by the scaling matrix. Furthermore, an algorithm for computing numerically orthogonal eigenvectors is sketched. This algorithm does not rely on the Gram-Schmidt process but requires conditions on the locus of eigenvalues.
reviewed by: Thomas Sonar
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 1443447
zbMATH Keywords: error analysis
zbMATH Keywords: triangular factorization
zbMATH Keywords: symmetric tridiagonal matrix
zbMATH Keywords: diagonal scaling matrices
zbMATH Keywords: algorithm
zbMATH Keywords: orthogonal eigenvectors
zbMATH Keywords: eigenvalues
author: Beresford N. Parlett
author: Inderjit S. Dhillon
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1443447