Fast accurate eigenvalue methods for graded positive definite matrices
type: Item
instance of: scholarly article
title: Fast accurate eigenvalue methods for graded positive definite matrices
zbMATH Open document ID: 0856.65038
author: Roy Mathias
published in: Numerische Mathematik
publication date: 1997-02-11T00:00:00Z
review text: If \(A\) is a positive definite matrix, and its condition number is much less than that of a diagonal matrix \(D\), then \(H=DAD\) is called a graded matrix. The Cholesky factorization of \(H\) is used to propose fast algorithms for the computation of the eigenvalues of \(H\). The eigenvalues can be computed to high relative accuracy and more efficiently than by Jacobi's method. In some cases the new methods can be four times faster than tridiagonalization methods.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 932010
zbMATH Keywords: positive definite matrix
zbMATH Keywords: condition number
zbMATH Keywords: graded matrix
zbMATH Keywords: Cholesky factorization
zbMATH Keywords: fast algorithms
zbMATH Keywords: eigenvalues
zbMATH Keywords: Jacobi's method
reviewed by: Plamen Yalamov
MaRDI profile type: Publication
full work available at URL: s002110050209
OpenAlex ID: W2081925639
DOI: 10.1007/S002110050209
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description: scientific article; zbMATH DE number 932010