Highly accurate symmetric eigenvalue decomposition and hyperbolic SVD
type: Item
instance of: scholarly article
title: Highly accurate symmetric eigenvalue decomposition and hyperbolic SVD
zbMATH Open document ID: 1030.65026
DOI: 10.1016/S0024-3795(02)00516-5
author: Ivan Slapničar
published in: Linear Algebra and its Applications
publication date: 2003-02-05T00:00:00Z
review text: In the computation of eigenvalues and singular values, the relative accuracy may vary widely. Here the author sets out to analyse when it is possible to compute the hyperbolic singular value decomposition (SVD) with high relative accuracy. He shows that a one-sided hyperbolically orthogonal Jacobi method is well suited for this task. This in turn yields an algorithm which even for the normal symmetric eigenvalue problem has higher relative accuracy than the usual QR and Jacobi methods. This is demonstrated on some numerical examples.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 1864806
zbMATH Keywords: hyperbolic singular value decomposition
zbMATH Keywords: symmetric eigenvalue problem
zbMATH Keywords: symmetric indefinition decomposition
zbMATH Keywords: Jacobi method
zbMATH Keywords: relative perturbation theory
zbMATH Keywords: high relative accuracy
zbMATH Keywords: algorithm
zbMATH Keywords: numerical examples
reviewed by: Hermann G. Matthies
describes a project that uses: LAPACK
MaRDI profile type: Publication
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full work available at URL: s0024-3795(02)00516-5
OpenAlex ID: W2009871339
description: scientific article; zbMATH DE number 1864806