Large sparse symmetric eigenvalue problems with homogeneous linear constraints: The Lanczos process with inner-outer iterations
type: Item
instance of: scholarly article
title: Large sparse symmetric eigenvalue problems with homogeneous linear constraints: The Lanczos process with inner-outer iterations
zbMATH Open document ID: 0948.65033
DOI: 10.1016/S0024-3795(99)00204-9
author: Gene H. Golub
author: Zhenyue Zhang
author: Hongyuan Zha
published in: Linear Algebra and its Applications
publication date: 2000-11-13T00:00:00Z
review text: Designing and analyzing inner-outer iteration algorithms for large sparse eigenproblems is largely an unsolved problem. The authors point out that they only touch the tip of the iceberg, and many issues still remain to be resolved. They study concrete examples of problems of this type with homogeneous linear constraints. Their goal is to compute extreme eigenvalues to certain accuracy with minimum total number of inner iteration steps. They develop two stopping criteria for the inner-outer Lanczos process and provide an analysis to explain the behavior of these two processes. A variety of numerical examples demonstrating the efficiency and accuracy of the proposed approaches is presented.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 1443453
zbMATH Keywords: large sparse eigenvalue problem
zbMATH Keywords: inner-outer iteration algorithms
zbMATH Keywords: extreme eigenvalues
zbMATH Keywords: numerical examples
reviewed by: R. P. Tewarson
describes a project that uses: CRAIG
describes a project that uses: JDQZ
describes a project that uses: LSQR
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1443453