Geodesic
Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem
Electronic transactions on numerical analysis, Tome 29 (2008)
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.
Classification : 65F15, 65F50, 15A18, 15A69
Keywords: multiparameter eigenvalue problem, two-parameter eigenvalue problem, harmonic extraction, refined extraction, Rayleigh-ritz, subspace method, saad's theorem, Jacobi-davidson 
@article{ETNA_2008__29__a8,
     author = {Hochstenbach,  Michiel E. and Plestenjak,  Bor},
     title = {Harmonic {Rayleigh-Ritz} extraction for the multiparameter eigenvalue problem},
     journal = {Electronic transactions on numerical analysis},
     year = {2008},
     volume = {29},
     zbl = {1171.65378},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__29__a8/}
}
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AU  - Plestenjak,  Bor
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JO  - Electronic transactions on numerical analysis
PY  - 2008
VL  - 29
UR  - http://geodesic.mathdoc.fr/item/ETNA_2008__29__a8/
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ID  - ETNA_2008__29__a8
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%0 Journal Article
%A Hochstenbach,  Michiel E.
%A Plestenjak,  Bor
%T Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem
%J Electronic transactions on numerical analysis
%D 2008
%V 29
%U http://geodesic.mathdoc.fr/item/ETNA_2008__29__a8/
%G en
%F ETNA_2008__29__a8
Hochstenbach,  Michiel E.; Plestenjak,  Bor. Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem. Electronic transactions on numerical analysis, Tome 29 (2008). http://geodesic.mathdoc.fr/item/ETNA_2008__29__a8/