Backward error bounds for constrained least squares problems
type: Item
instance of: scholarly article
title: Backward error bounds for constrained least squares problems
zbMATH Open document ID: 0930.65040
DOI: 10.1023/A:1022385611904
author: Anthony J. Cox
author: Nicholas J. Higham
published in: BIT
publication date: 2000-02-16T00:00:00Z
review text: An upper bound on the normwise backward error of an approximate solution to the equality constrained least squares problem is given. This is an attempt to answer to the question ``How much perturbations have to be registered, in order to obtain a sufficiently good approximate solution?''. Summarizing normwise backward error results for a linear system and for the least squares minimization over a sphere, upper and lower bounds for the backward errors are derived. Also some results, obtained from numerical experiments are given, to illustrate the practical effectiveness of the proposed way to reduce the size of the upper bound.
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 1309450
zbMATH Keywords: backward error bounds
zbMATH Keywords: overdetermined systems
zbMATH Keywords: backward stability
zbMATH Keywords: numerical examples
zbMATH Keywords: upper bound
zbMATH Keywords: equality constrained least squares problem
reviewed by: Tzvetan Semerdjiev
describes a project that uses: GQTPAR
describes a project that uses: testmatrix
describes a project that uses: LAPACK
describes a project that uses: mctoolbox
MaRDI profile type: Publication
full work available at URL: a:1022385611904
OpenAlex ID: W2127345882
Wikidata QID: Q56998885
description: scientific article; zbMATH DE number 1309450