Reusing and Updating Preconditioners for Sequences of Matrices

For sequences of related linear systems, the computation of a preconditioner for every system can be expensive. Often a fixed preconditioner is used, but this may not be effective as the matrix changes. This research examines the benefits of both reusing and recycling preconditioners, with special focus on ILUTP and factorized sparse approximate inverses and proposes an update that we refer to as a sparse approximate map or SAM update. Analysis of the residual and eigenvalues of the map will be provided. Applications include the Quantum Monte Carlo method, model reduction, oscillatory hydraulic tomography, diffuse optical tomography, and Helmholtz-type problems.

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

2015

Author dc:creator

• Grim-McNally, Arielle Katherine

Chair dc:contributor.committeechair

• de Sturler, Eric

Committee members dc:contributor.committeemember

• Gugercin, Serkan
• Chung, Julianne

• Recycling Preconditioners
• Preconditioners
• Sparse Approximate Map
• Incomplete LU Decomposition
• Sparse Approximate Inverse
• Factorized Sparse Approximate Inverse
• Krylov Methods

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Dc Identifier Other

vt_gsexam:5645

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/52945