Incomplete factorization preconditioning for linear least squares problems

A new family of preconditioners for conjugate gradient-like iterative methods applied to large sparse linear least squares problems, $min\Vert Ax-b\Vert\sb2$, is proposed. The family is based on incomplete Gram-Schmidt (IGS) factorizations of A. Particular attention has been given to the following members of the family: Incomplete Classical Gram-Schmidt (ICGS), Incomplete Modified Gram-Schmidt (IMGS) and Compressed Incomplete Modified Gram-Schmidt (CIMGS) factorizations. The numerical properties of each of these methods have been considered as well as the relationships between the methods concerning the preservation of sparsity, computational efficiency and the quality of the preconditioner. The implementation of these methods has been investigated and all of the important family members have been coded. One of the important topics in this portion of the dissertation is the careful symbolic analysis of the production of the preconditioner and its use during the incomplete factorization phase to avoid excessive unnecessary work.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Wang, Xiaoge

Contributors dc:contributor

• Gallivan, Kyle A.

• Mathematics
• Computer Science

Statement dc:rights

• Copyright 1994 Wang, Xiaoge

Language dc:language

eng

Identifier

AAI9416449
(UMI)AAI9416449

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/20281