New bounds for perturbation of the orthogonal projection
type: Item
instance of: scholarly article
title: New bounds for perturbation of the orthogonal projection
zbMATH Open document ID: 1266.65064
author: Bingxiang Li
author: Wen Li
author: Lu-Bin Cui
published in: Calcolo
publication date: 2013-04-15T00:00:00Z
review text: For a matrix \(M\) with Moore-Penrose inverse \(M^\dag\), define the projection matrix \(P_M=MM^\dag\). Consider a matrix \(A\) and its perturbation \(B\) that can be additive (\(B=A+E\)) or multiplicative (\(B=D_1AD_2\)) then this paper gives a bound for \(\|P_A-P_B\|\) for a general unitarily invariant norm. The analysis is based on the singular value decomposition of the matrix \(A\) and is a slight improvement over known estimates. The disadvantage is however that the bounds not only assume some knowledge of the perturbing matrices and the singular values of \(A\) but they also involve the singular vectors.
reviewed by: Adhemar Bultheel
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 6153976
zbMATH Keywords: singular value decomposition
zbMATH Keywords: orthogonal projection
zbMATH Keywords: additive perturbation
zbMATH Keywords: multiplicative perturbation
zbMATH Keywords: Moore-Penrose inverse
MaRDI profile type: Publication
full work available at URL: s10092-012-0058-0
OpenAlex ID: W2086872883
cites work: Q5690490
cites work: Some new perturbation bounds for subunitary polar factors
cites work: On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems
cites work: Perturbation analysis for the eigenproblem of periodic matrix pairs
DOI: 10.1007/S10092-012-0058-0
description: scientific article; zbMATH DE number 6153976