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Conditions for convergence of the restarted and augmented GMRES method
dc.contributor.advisorZítko, Jan
dc.creatorNádhera, David
dc.date.accessioned2017-04-20T16:54:05Z
dc.date.available2017-04-20T16:54:05Z
dc.date.issued2009
dc.identifier.urihttp://hdl.handle.net/20.500.11956/27658
dc.description.abstractThe GMRES method is one of the most useful methods for solving a system of linear algebraic equations with nonsymmetric matrix. So on, many bounds for the residual norm have been derived, that can give us information about the convergence or possible stagnation of the method. A generalization of the GMRES method is the augmented GMRES method. In this paper we will analyze the implementation of augmented GMRES method proposed by Morgan. In these consequences we will be interested in how precise harmonic Ritz vectors approximate the eigenvectors belonging to the smallest in magnitude eigenvalues. We generalize some previous results concerning the convergence of restarted GMRES method for the case of augmented GMRES method. This is the rst contribution of the work. Another main point will be numerical testing and comparing of the bounds for restarted and augmented GMRES and an attempt to state a criterion, when it is suitable to stop the improvement of augmenting vectors, i. e. apply the augmented GMRES method without additional computations.en_US
dc.languageČeštinacs_CZ
dc.language.isocs_CZ
dc.publisherUniverzita Karlova, Matematicko-fyzikální fakultacs_CZ
dc.titlePodmínky pro konvergenci restartované a rozšířené metody GMREScs_CZ
dc.typediplomová prácecs_CZ
dcterms.created2009
dcterms.dateAccepted2009-09-22
dc.description.departmentDepartment of Numerical Mathematicsen_US
dc.description.departmentKatedra numerické matematikycs_CZ
dc.description.facultyFaculty of Mathematics and Physicsen_US
dc.description.facultyMatematicko-fyzikální fakultacs_CZ
dc.identifier.repId48142
dc.title.translatedConditions for convergence of the restarted and augmented GMRES methoden_US
dc.contributor.refereeStrakoš, Zdeněk
dc.identifier.aleph001139232
thesis.degree.nameMgr.
thesis.degree.levelnavazující magisterskécs_CZ
thesis.degree.disciplineNumerická a výpočtová matematikacs_CZ
thesis.degree.disciplineNumerical and computational mathematicsen_US
thesis.degree.programMatematikacs_CZ
thesis.degree.programMathematicsen_US
uk.thesis.typediplomová prácecs_CZ
uk.taxonomy.organization-csMatematicko-fyzikální fakulta::Katedra numerické matematikycs_CZ
uk.taxonomy.organization-enFaculty of Mathematics and Physics::Department of Numerical Mathematicsen_US
uk.faculty-name.csMatematicko-fyzikální fakultacs_CZ
uk.faculty-name.enFaculty of Mathematics and Physicsen_US
uk.faculty-abbr.csMFFcs_CZ
uk.degree-discipline.csNumerická a výpočtová matematikacs_CZ
uk.degree-discipline.enNumerical and computational mathematicsen_US
uk.degree-program.csMatematikacs_CZ
uk.degree-program.enMathematicsen_US
thesis.grade.csVýborněcs_CZ
thesis.grade.enExcellenten_US
uk.abstract.enThe GMRES method is one of the most useful methods for solving a system of linear algebraic equations with nonsymmetric matrix. So on, many bounds for the residual norm have been derived, that can give us information about the convergence or possible stagnation of the method. A generalization of the GMRES method is the augmented GMRES method. In this paper we will analyze the implementation of augmented GMRES method proposed by Morgan. In these consequences we will be interested in how precise harmonic Ritz vectors approximate the eigenvectors belonging to the smallest in magnitude eigenvalues. We generalize some previous results concerning the convergence of restarted GMRES method for the case of augmented GMRES method. This is the rst contribution of the work. Another main point will be numerical testing and comparing of the bounds for restarted and augmented GMRES and an attempt to state a criterion, when it is suitable to stop the improvement of augmenting vectors, i. e. apply the augmented GMRES method without additional computations.en_US
uk.publication.placePrahacs_CZ
uk.grantorUniverzita Karlova, Matematicko-fyzikální fakulta, Katedra numerické matematikycs_CZ
dc.identifier.lisID990011392320106986


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