Condition numbers and perturbation of the weighted Moore--Penrose inverse and weighted linear least squares problem.
type: Item
instance of: scholarly article
title: Condition numbers and perturbation of the weighted Moore--Penrose inverse and weighted linear least squares problem.
zbMATH Open document ID: 1044.15005
DOI: 10.1016/S0096-3003(02)00437-X
author: Dingkun Wang
author: Yimin Wei
published in: Applied Mathematics and Computation
publication date: 2003-11-25T00:00:00Z
review text: Given positive definite matrices \(M\) and \(N\) of orders \(m\) and \(n\) respectively, the ``weighted'' Moore-Penrose inverse \(G\) of an \(m\times n\) matrix \(A\) is the unique solution of \(AGA=A\), \(GAG=G\), \((MAG)^* =MAG\), and \((NGA)^* =NGA\). This paper derives formulae for condition numbers of the weighted Moore-Penrose inverse and for similarly weighted condition numbers of singular linear systems \(Ax=b\), and gives a perturbation analysis of the weighted least squares problem in the case in which the perturbed and unperturbed coefficient matrices have the same rank.
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A06
zbMATH DE Number: 2008951
zbMATH Keywords: condition number
zbMATH Keywords: weighted Moore-Penrose inverse
zbMATH Keywords: least squares
zbMATH Keywords: perturbation
zbMATH Keywords: singular linear systems
reviewed by: Alan L. Andrew
MaRDI profile type: Publication
cites work: On the solution of the linear least squares problems and pseudo-inverses
cites work: Q4061081
cites work: Q4030499
cites work: Perturbation identities for regularized Tikhonov inverses and weighted pseudo- inverses
cites work: Condition numbers and their condition numbers
cites work: Generalizing the Singular Value Decomposition
cites work: Perturbation bound of singular linear systems
cites work: Expression for the perturbation of the weighted Moore-Penrose inverse
cites work: The representation and approximation for the weighted Moore-Penrose inverse
cites work: Representations for Moore-Penrose inverses in Hilbert spaces
cites work: PCR algorithm for parallel computing minimum-norm \((T)\) least-squares \((S)\) solution of inconsistent linear equations
full work available at URL: s0096-3003(02)00437-x
OpenAlex ID: W2110893654
description: scientific article; zbMATH DE number 2008951