Abstract
dc:description.abstractThe Biconjugate Gradient (BiCG) method is an iterative Krylov subspace method that utilizes a 3-term recurrence. BiCG is the basis of several very popular methods, such as BiCGStab. The short recurrence makes BiCG preferable to other Krylov methods because of decreased memory usage and CPU time. However, BiCG does not satisfy any optimality conditions and it has been shown that for up to n/2-1 iterations, a special choice of the left starting vector can cause BiCG to follow {em any} 3-term recurrence. Despite this apparent sensitivity, BiCG often converges well in practice. This paper seeks to explain why BiCG converges so well, and what conditions can cause BiCG to behave poorly. We use tools such as the singular value decomposition and eigenvalue decomposition to establish bounds on the residuals of BiCG and make links between BiCG and optimal Krylov methods.
Degree
thesis:*- 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
- 2013
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Renardy, Marissa
- Chair dc:contributor.committeechair
-
- de Sturler, Eric
- Committee members dc:contributor.committeemember
-
- Rossi, John F.
- Linnell, Peter A.
Subjects
dc:subject × 4Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- vt_gsexam:934
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/50922