Second-order optimality condition for \({\Delta}H\)-matrices
type: Item
instance of: scholarly article
title: Second-order optimality condition for \({\Delta}H\)-matrices
zbMATH Open document ID: 1046.15022
published in: BIT
publication date: 2004-06-11T00:00:00Z
review text: A \(\Delta H\) matrix \(A\) is a square matrix that can be written as \(A=D+DH-HD\), for certain Hermitian \(H\) and diagonal \(D\). \textit{A. Ruhe} [BIT 27, 585--598 (1987; Zbl 0636.15017)] gave a necessary and sufficient condition to solve the problem of finding a normal matrix \(N\) realizing the Frobenius distance from \(A\) to the variety of normal matrices. In the paper under review, the author gives a new characterization of the second-order optimality condition given by Ruhe, in terms of an eigenvalue problem.
reviewed by: Martín Argerami
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 2073453
zbMATH Keywords: normal matrix
zbMATH Keywords: optimality condition
zbMATH Keywords: perturbation
zbMATH Keywords: local minimum
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: approximation
zbMATH Keywords: Frobenius distance
author: L. László
MaRDI profile type: Publication
full work available at URL: b:bitn.0000007050.12171.aa
OpenAlex ID: W2012058927
DOI: 10.1023/B:BITN.0000007050.12171.AA
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description: scientific article; zbMATH DE number 2073453