Return to search

Analysis of the BiCG Method

The 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. / Master of Science

Identiferoai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/50922
Date31 May 2013
CreatorsRenardy, Marissa
ContributorsMathematics, de Sturler, Eric, Rossi, John F., Linnell, Peter A.
PublisherVirginia Tech
Source SetsVirginia Tech Theses and Dissertation
Detected LanguageEnglish
TypeThesis
FormatETD, application/pdf
RightsIn Copyright, http://rightsstatements.org/vocab/InC/1.0/

Page generated in 0.002 seconds