Improving eigenvalue bounds using extra bounds
type: Item
instance of: scholarly article
title: Improving eigenvalue bounds using extra bounds
zbMATH Open document ID: 0574.15010
DOI: 10.1016/0024-3795(85)90209-5
author: Jorma K. Merikoski
author: Henry Wolkowicz
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
review text: In previous papers, the authors (with others) have obtained very good bounds for various functions of the eigenvalues of an \(n\times n\) complex matrix with real eigenvalues \(\lambda_ 1\geq \lambda_ 2\geq...\geq \lambda_ n\)- in fact the best bounds when using only n, tr A and tr \(A^ 2\). In this paper, with A Hermitian, the authors use besides the information given by the diagonal elements and present a program to obtain the best possible upper bound for \(\lambda_ k\) and the best lower bound for \(\lambda_{k+1}\), given n, tr A, tr \(A^ 2\) and the ordered diagonal elements. This program is illustrated by several examples. Other bounds are obtained invoking some matrix norms.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 3916479
zbMATH Keywords: eigenvalue bounds for matrix functions
zbMATH Keywords: Hermitian matrix
zbMATH Keywords: Karush-Kuhn- Tucker conditions
MaRDI profile type: Publication
full work available at URL: 0024-3795(85)90209-5
OpenAlex ID: W2077555649
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description: scientific article; zbMATH DE number 3916479