Accurate ordering of eigenvectors and singular vectors without eigenvalues and singular values.
type: Item
instance of: scholarly article
title: Accurate ordering of eigenvectors and singular vectors without eigenvalues and singular values.
zbMATH Open document ID: 1033.65017
DOI: 10.1016/S0024-3795(03)00537-8
author: D. Massart
published in: Linear Algebra and its Applications
publication date: 2003-11-19T00:00:00Z
review text: The author identifies a structural property of an eigenvector of a symmetric tridiagonal matrix which can be used to rank and ordering eigenvectors without knowing the eigenvalues. This is extended to singular vectors of bidiagonal matrices. These procedures do not require floating-point operations and hence are immune from round-off errors. The paper proposes a simple but powerful method for testing of computed eigensolutions and the singular value decomposition.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 47B36
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 34L16
zbMATH DE Number: 2005989
zbMATH Keywords: eigenvalues
zbMATH Keywords: singular values
zbMATH Keywords: eigenvectors
zbMATH Keywords: singular vectors
zbMATH Keywords: symmetric tridiagonal matrices
zbMATH Keywords: Jacobi matrices
zbMATH Keywords: bidiagonal matrices
zbMATH Keywords: parallel computing
zbMATH Keywords: Sturm sequences
zbMATH Keywords: Sturm-Liouville theory
zbMATH Keywords: Sylvester-Jacobi inertia
zbMATH Keywords: Software testing and validation
zbMATH Keywords: ordering
zbMATH Keywords: singular value decomposition
reviewed by: Nicholas Karampetakis
describes a project that uses: LAPACK
MaRDI profile type: Publication
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full work available at URL: s0024-3795(03)00537-8
OpenAlex ID: W2154611179
description: scientific article; zbMATH DE number 2005989