Analysis of the BiCG Method

dc.contributor.authorRenardy, Marissaen
dc.contributor.committeechairde Sturler, Ericen
dc.contributor.committeememberRossi, John F.en
dc.contributor.committeememberLinnell, Peter A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-11-23T07:00:09Zen
dc.date.available2014-11-23T07:00:09Zen
dc.date.issued2013-05-31en
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.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:934en
dc.identifier.urihttp://hdl.handle.net/10919/50922en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectKrylov methodsen
dc.subjectBiCGen
dc.subjectGMRESen
dc.subjectFOMen
dc.titleAnalysis of the BiCG Methoden
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen
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