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Stagnation of GMRES

dc.contributor.authorZavorin, Ilyaen_US
dc.contributor.authorO'Leary, Dianne P.en_US
dc.contributor.authorElman, Howarden_US
dc.description.abstractWe study problems for which the iterative method \gmr for solving linear systems of equations makes no progress in its initial iterations. Our tool for analysis is a nonlinear system of equations, the stagnation system, that characterizes this behavior. For problems of dimension 2 we can solve this system explicitly, determining that every choice of eigenvalues leads to a stagnating problem for eigenvector matrices that are sufficiently poorly conditioned. We partially extend this result to higher dimensions for a class of eigenvector matrices called extreme. We give necessary and sufficient conditions for stagnation of systems involving unitary matrices, and show that if a normal matrix stagnates then so does an entire family of nonnormal matrices with the same eigenvalues. Finally, we show that there are real matrices for which stagnation occurs for certain complex right-hand sides but not for real ones. (Also UMIACS-TR-2001-74)en_US
dc.format.extent361139 bytes
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-4296en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-2001-74en_US
dc.titleStagnation of GMRESen_US
dc.typeTechnical Reporten_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtUMIACS Technical Reportsen_US

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