Bisection acceleration for the symmetric tridiagonal eigenvalue problem
type: Item
instance of: scholarly article
title: Bisection acceleration for the symmetric tridiagonal eigenvalue problem
zbMATH Open document ID: 0947.65043
DOI: 10.1023/A:1019146505291
author: Elliot Linzer
author: Victor Y. Pan
published in: Numerical Algorithms
publication date: 2000-10-22T00:00:00Z
review text: Eigenvalues in an interval for a symmetric tridiagonal matrix are computed. The interval is divided using a double exponential sieve, giving one very short interval and one with a good isolation ratio, which guarantees a rapid convergence of a Newton iteration. A complexity analysis is given, which shows that this improves on the traditional bisection algorithm, and this is illustrated on numerical examples.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 1398777
zbMATH Keywords: convergence acceleration
zbMATH Keywords: eigenvalues
zbMATH Keywords: symmetric tridiagonal matrix
zbMATH Keywords: convergence
zbMATH Keywords: Newton iteration
zbMATH Keywords: complexity
zbMATH Keywords: bisection algorithm
zbMATH Keywords: numerical examples
reviewed by: Axel Ruhe
MaRDI profile type: Publication
full work available at URL: a:1019146505291
OpenAlex ID: W1651652452
description: scientific article; zbMATH DE number 1398777