Restarting the Lanczos algorithm for large eigenvalue problems and linear equations.

We are interested in computing eigenvalues and eigenvectors of large matrices and in solving large systems of linear equations. Restarted versions of both the symmetric and nonsymmetric Lanczos algorithms are given. For the symmetric case, we give a method called Lan-DR that simultaneously solves linear equations and computes eigenvalues and eigenvectors. The use of approximate eigenvectors deflates eigenvalues. Maintaining the orthogonality of the Lanczos vectors is a concern. We suggest an approach that is a combination of Parlett and Scott's idea of selective orthogonalization and Simon's partial orthogonalization. For linear systems with multiple right-sides, eigenvectors computed during the solution of the first right-hand side can be used to give much faster convergence of the second and subsequent right-hand sides. A restarted version of the nonsymmetric Lanczos algorithm is developed. Both the right and left eigenvectors are computed while systems of linear equations are solved. We also investigate a restarted two-sided Arnoldi. We compare expense and stability of this approach with restarted nonsymmetric Lanczos.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Doctoral

Grantor

Baylor University.

Year dc:date.issued

2008

Author dc:creator

• Nicely, Dywayne A.

Advisor dc:contributor.advisor

• Morgan, Ronald Benjamin, 1958-

• Eigenvalues.
• Algorithms.
• Eigenvectors.
• Linear systems.
• Iterative methods (Mathematics)
• Orthogonalization methods.

Statement dc:rights

• Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/2104/5219

OAI identifier oai:identifier

oai:baylor-ir.tdl.org:2104/5219