Accuracy and stability of the null space method for solving the equality constrained least squares problem
type: Item
instance of: scholarly article
title: Accuracy and stability of the null space method for solving the equality constrained least squares problem
zbMATH Open document ID: 0924.65033
DOI: 10.1023/A:1022365107361
author: Anthony J. Cox
author: Nicholas J. Higham
published in: BIT
publication date: 1999-11-10T00:00:00Z
review text: The stability of null space methods for solving the linear least squares problem subject to equality constraints (the LSE problem) is proved via a detailed rounding error analysis. A normwise perturbation theory for the LSE problem is presented. A perturbation bound is derived but it is shown that the bound does not yield a condition number for the LSE problem, since it is not attainable. By modifying the analysis an almost sharp bound is derived that yields a quantity that is within a small constant factor of the condition number for the LSE problem. The quantity LSE\(_-\)err is determined which can be used as an approximate forward error bound for the null space method for solving the LSE problem and, in particular, for use with the driver routine ``xgglse.f'' in LAPACK.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65G50
zbMATH DE Number: 1275241
zbMATH Keywords: stability
zbMATH Keywords: null space methods
zbMATH Keywords: linear least squares problem
zbMATH Keywords: rounding error analysis
zbMATH Keywords: condition number
zbMATH Keywords: forward error bound
zbMATH Keywords: LAPACK
reviewed by: Florica Luban
describes a project that uses: LAPACK
describes a project that uses: mctoolbox
MaRDI profile type: Publication
Wikidata QID: Q56998882
description: scientific article; zbMATH DE number 1275241