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dc.contributor.authorSosonkina, Mashaen_US
dc.contributor.authorWatson, Layne T.en_US
dc.contributor.authorKapania, Rakesh Ken_US
dc.date.accessioned2013-05-28T20:43:25Zen_US
dc.date.accessioned2013-06-19T14:36:34Z
dc.date.available2013-05-28T20:43:25Zen_US
dc.date.available2013-06-19T14:36:34Z
dc.date.issued1996-05-01
dc.identifierhttp://eprints.cs.vt.edu/archive/00000448/en_US
dc.identifier.urihttp://hdl.handle.net/10919/19899
dc.descriptionGMRES(k) is widely used for solving nonsymmetric linear systems. However, it is inadequate either when it converges only for k close to the problem size or when numerical error in the modified Gram-Schmidt process used in the GMRES orthogonalization phase dramatically affects the algorithm performance. An adaptive version of GMRES(k) which tunes the restart value k based on criteria estimating the GMRES conversion rate for the given problem is proposed here. This adaptive GMRES(k) procedure outperforms standard GMRES(k), several other GMRES-like methods, and QMR on actual large scale sparse structural mechanics postbuckling and analog circuit simulation problems. There are some applications, such as homotopy methods for high Reynolds number viscous flows, solid mechanics postbuckling analysis, and analog circuit simulation, where very high accuracy in the linear system solutions is essential. In this context, the modified Gram-Schmidt process in GMRES can fail causing the entire GMRES iteration to fail. It is shown that the adaptive GMRES(k) with the orthogonalization performed by Householder transformations succeeds whenever GMRES(k) with the orthogonolization performed by the modified Gram-Schmidt process fails, and the extra cost of computing Householder transformations is justified for these applications.en_US
dc.format.mimetypeapplication/postscripten_US
dc.publisherDepartment of Computer Science, Virginia Polytechnic Institute & State Universityen_US
dc.relation.ispartofHistorical Collection(Till Dec 2001)en_US
dc.titleA New Adaptive GMRES Algorithm for Achieving High Accuracyen_US
dc.typeTechnical reporten_US
dc.identifier.trnumberTR-96-09en_US
dc.type.dcmitypeTexten_US
dc.identifier.sourceurlhttp://eprints.cs.vt.edu/archive/00000448/01/TR-96-09.ps


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