The nearest definite pair for the Hermitian generalized eigenvalue problem
type: Item
instance of: scholarly article
title: The nearest definite pair for the Hermitian generalized eigenvalue problem
zbMATH Open document ID: 0947.65042
DOI: 10.1016/S0024-3795(99)00026-9
author: Sheung Hun Cheng
author: Nicholas J. Higham
published in: Linear Algebra and its Applications
publication date: 2000-03-21T00:00:00Z
review text: Given a pair \((A,B)\) of Hermitian matrices of the same order, the authors give formulae for the nearest pair of Hermitian matrices that has a Crawford number greater or equal to a given positive value. The result is expressed in terms of the inner numerical radius associated with the field of values. Then they show how to exploit the result in order to solve the generalized eigenvalue problem \(Ax=\lambda Bx\) with nearly singular \(B\). The paper includes the algorithm and numerical examples.
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 1419860
zbMATH Keywords: field of values
zbMATH Keywords: Hermitian matrices
zbMATH Keywords: Crawford number
zbMATH Keywords: numerical radius
zbMATH Keywords: generalized eigenvalue problem
zbMATH Keywords: algorithm
zbMATH Keywords: numerical examples
Wikidata QID: Q56998899
reviewed by: Z. Dostál
describes a project that uses: PDFIND
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1419860