The expression of the generalized Bott-Duffin inverse and its perturbation theory
type: Item
instance of: scholarly article
title: The expression of the generalized Bott-Duffin inverse and its perturbation theory
zbMATH Open document ID: 1030.15006
DOI: 10.1016/S0096-3003(01)00204-1
author: Yifeng Xue
author: Guoliang Chen
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: It is well-known that the Boot-Duffin inverse \(A_L^{-1}=P_L(AP_L+I-P_L)^{-1}\) gives the solution of the constrained system \(Ax+y=b\), where \(x \in L\), \(y \in L^{\perp}\) being \(L\) a subspace of \({\mathbb C}^{n}\), \(L^{\perp}\) its orthogonal, \(A \in {\mathbb C}^{n \times n}\), \(b \in {\mathbb C}^{n}\) and \(P_L\) the projection on \(L\). In this work, an extension of \(A_L^{-1}\) is given by the generalized Boot-Duffin inverse \(A^{(+)}_L = P_L(AP_L+I-P_L)^+\) where \((AP_L+I-P_L)^+\) means the Moore-Penrose inverse of a block of \(AP_L+I-P_L\). Applying this new expression for \(A^{(+)}_L\) a perturbation analysis is developed for the generalized Boot-Duffin inverse.
reviewed by: Néstor Thome
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A06
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 1861222
zbMATH Keywords: Boot-Duffin inverse
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: least squares
zbMATH Keywords: L-zero matrix
zbMATH Keywords: perturbation analysis
MaRDI profile type: Publication
cites work: Q4061081
cites work: On the Algebra of Networks
cites work: Perturbation theory for the generalized Bott-Duffin inverse and its applications
cites work: Perturbation analysis of the least squares solution in Hilbert spaces
cites work: Perturbation analysis for the operator equation \(Tx=b\) in Banach spaces
cites work: The expression of the generalized inverse of the perturbed operator under Type I perturbation in Hilbert spaces
cites work: The generalized Bott-Duffin inverse and its applications
cites work: Q3998482
full work available at URL: s0096-3003(01)00204-1
OpenAlex ID: W2003502899
description: scientific article; zbMATH DE number 1861222