Recycling Bi-Lanczos Algorithms: BiCG, CGS, and BiCGSTAB

Engineering problems frequently require solving a sequence of dual linear systems. This paper introduces recycling BiCG, that recycles the Krylov subspace from one pair of linear systems to the next pair. Augmented bi-Lanczos algorithm and modified two-term recurrence are developed for using the recycle space. Recycle space is built from the approximate invariant subspace corresponding to eigenvalues close to the origin. Recycling approach is extended to the CGS and the BiCGSTAB algorithms. Experiments on a convection-diffusion problem give promising results.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2009

Author dc:creator

• Ahuja, Kapil

Chair dc:contributor.committeechair

• de Sturler, Eric

Committee members dc:contributor.committeemember

• Gugercin, Serkan
• Borggaard, Jeffrey T.
• Beattie, Christopher A.

• Krylov subspace recycling
• Petrov-Galerkin formulation
• bi-Lanczos method

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-08252009-161256

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/34765