Current inverse iteration software can fail
type: Item
instance of: scholarly article
title: Current inverse iteration software can fail
zbMATH Open document ID: 0918.65025
DOI: 10.1007/BF02510409
author: Inderjit S. Dhillon
published in: BIT
publication date: 1999-08-17T00:00:00Z
review text: The author discusses various issues arising in the implementation of inverse iteration using reorthogonaliszation to compute eigenvectors of real symmetric matrices when the eigenvalues agree to more than three digits relative to the norm. Both theoretical and empirical failures of these implementations in EISEPACK and LAPACK are demonstrated. Finally, alternate approaches to the unresolved issues are mentioned.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F25
Mathematics Subject Classification ID: 65Y15
zbMATH DE Number: 1251186
zbMATH Keywords: inverse iteration
zbMATH Keywords: reorthogonaliszation
zbMATH Keywords: eigenvectors
zbMATH Keywords: real symmetric matrices
zbMATH Keywords: eigenvalues
zbMATH Keywords: EISEPACK
zbMATH Keywords: LAPACK
describes a project that uses: LAPACK
describes a project that uses: CLAPACK
describes a project that uses: EISPACK
reviewed by: Prem Narain
MaRDI profile type: Publication
cites work: Q4841244
cites work: Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices
cites work: On Computing an Eigenvector of a Tridiagonal Matrix. Part I: Basic Results
cites work: Q3703189
cites work: Unitary Triangularization of a Nonsymmetric Matrix
cites work: Computing an Eigenvector with Inverse Iteration
cites work: Improving the Accuracy of Inverse Iteration
cites work: Q4348515
cites work: Fernando's solution to Wilkinson's problem: An application of double factorization
cites work: Inverse Iteration, Ill-Conditioned Equations and Newton’s Method
cites work: Matrix eigensystem routines - EISPACK guide. 2nd ed
cites work: The Calculation of the Eigenvectors of Codiagonal Matrices
cites work: Q5674306
description: scientific article; zbMATH DE number 1251186