Perturbation of the least squares problem
type: Item
instance of: scholarly article
title: Perturbation of the least squares problem
zbMATH Open document ID: 0711.15005
DOI: 10.1016/0024-3795(90)90316-5
author: Musheng Wei
published in: Linear Algebra and its Applications
publication date: 1990-01-01T00:00:00Z
review text: Let \(\bar A=A+\delta A\), \(\bar b=b+\delta b\) where A is a matrix, b is a vector, and \(\delta\) A, \(\delta\) b are perturbations in A and b. Let \(x_{LS}\) be the minimum norm least squares solution of \(Ax=b\), and \(\bar x_{LS}\) the minimum norm least squares solution of \(\bar Ax=\bar b\). This paper shows that there exists a least squares solution \(\hat x\) to \(Ax=b\) for which \(\| \hat x-\bar x_{LS}\|\) satisfies an error estimate in terms of \(\{\| A\|,\| b\|,\| \delta A\|,\| \delta b\|,\| \bar x_{LS}\|,\| \hat x\|,\| b-Ax_{LS}\| \}\).
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 4168842
zbMATH Keywords: minimum norm least squares solution
zbMATH Keywords: error estimate
reviewed by: Stephen L. Campbell
MaRDI profile type: Publication
full work available at URL: 0024-3795(90)90316-5
OpenAlex ID: W2087090392
cites work: Rang revealing QR factorizations
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description: scientific article; zbMATH DE number 4168842