Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem

We study harmonic and refined extraction methods for the multiparameter eigenvalue problem. These techniques are generalizations of their counterparts for the standard and generalized eigenvalue problem. The methods aim to approximate interior eigenpairs, generally more accurately than the standard...

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Published inElectronic transactions on numerical analysis Vol. 29; p. 81
Main Authors Hochstenbach, Michiel E, Plestenjak, Bor
Format Journal Article
LanguageEnglish
Published Institute of Computational Mathematics 01.12.2007
Subjects
Approximation theory
Eigenvalues
Evaluation
Mathematical research
Methods
Netherlands
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ISSN1068-9613
1097-4067

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Abstract We study harmonic and refined extraction methods for the multiparameter eigenvalue problem. These techniques are generalizations of their counterparts for the standard and generalized eigenvalue problem. The methods aim to approximate interior eigenpairs, generally more accurately than the standard extraction does. We study their properties and give Saad-type theorems. The processes can be combined with any subspace expansion approach, for instance a Jacobi-Davidson type technique, to form a subspace method for multiparameter eigenproblems of high dimension. Key words. multiparameter eigenvalue problem, two-parameter eigenvalue problem, harmonic extraction, refined extraction, Rayleigh-Ritz, subspace method, Saad's theorem, Jacobi-Davidson AMS subject classifications. 65F15, 65F50, 15A18, 15A69
AbstractList We study harmonic and refined extraction methods for the multiparameter eigenvalue problem. These techniques are generalizations of their counterparts for the standard and generalized eigenvalue problem. The methods aim to approximate interior eigenpairs, generally more accurately than the standard extraction does. We study their properties and give Saad-type theorems. The processes can be combined with any subspace expansion approach, for instance a Jacobi-Davidson type technique, to form a subspace method for multiparameter eigenproblems of high dimension.
We study harmonic and refined extraction methods for the multiparameter eigenvalue problem. These techniques are generalizations of their counterparts for the standard and generalized eigenvalue problem. The methods aim to approximate interior eigenpairs, generally more accurately than the standard extraction does. We study their properties and give Saad-type theorems. The processes can be combined with any subspace expansion approach, for instance a Jacobi-Davidson type technique, to form a subspace method for multiparameter eigenproblems of high dimension. Key words. multiparameter eigenvalue problem, two-parameter eigenvalue problem, harmonic extraction, refined extraction, Rayleigh-Ritz, subspace method, Saad's theorem, Jacobi-Davidson AMS subject classifications. 65F15, 65F50, 15A18, 15A69
Audience Academic
Author Hochstenbach, Michiel E
Plestenjak, Bor
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Snippet We study harmonic and refined extraction methods for the multiparameter eigenvalue problem. These techniques are generalizations of their counterparts for the...
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StartPage 81
SubjectTerms Approximation theory
Eigenvalues
Evaluation
Mathematical research
Methods
Title Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem
Volume 29
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