Bounds for perturbed solutions of linear operator equations in Hilbert space.
type: Item
instance of: scholarly article
title: Bounds for perturbed solutions of linear operator equations in Hilbert space.
zbMATH Open document ID: 1038.47005
DOI: 10.1016/S0096-3003(01)00193-X
author: J. Ding
author: Yimin Wei
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: Let \(X\), \(Y\) be two Hilbert spaces and \(A: X\to Y\) be a bounded linear operator with closed range. The authors consider the system of one operator equation \(Ax= b\) and the perturbed equation \((A+ E)y= b+e\). Under the assumption that the system is consistent, they present lower and upper bounds on relative errors for perturbed solutions. Perturbation results on relative errors are also given for weighted least squares problems with the help of weighted generalized inverses.
Mathematics Subject Classification ID: 47A50
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 1861212
zbMATH Keywords: weighted least-square solution
zbMATH Keywords: weighted generalized inverse
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
cites work: Q3207128
cites work: Lower and upper bounds in the perturbation of general linear algebraic equations
cites work: Extensions and Applications of the Householder Algorithm for Solving Linear Least Squares Problems
cites work: Q4001758
cites work: Expression for the perturbation of the weighted Moore-Penrose inverse
full work available at URL: s0096-3003(01)00193-x
OpenAlex ID: W2003121772
description: scientific article; zbMATH DE number 1861212