Hochstenbach, Michiel E.; Plestenjak, Bor Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem. (English) Zbl 1171.65378 ETNA, Electron. Trans. Numer. Anal. 29(2007-2008), 81-96 (2008). Summary: 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 meth- ods 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. Cited in 10 Documents MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 65F50 Computational methods for sparse matrices 15A18 Eigenvalues, singular values, and eigenvectors 15A69 Multilinear algebra, tensor calculus Keywords:multiparameter eigenvalue problem; two-parameter eigenvalue problem; harmonic extraction; refined extraction; Rayleigh-Ritz; subspace method; Saad’s theorem; Jacobi-Davidson PDFBibTeX XMLCite \textit{M. E. Hochstenbach} and \textit{B. Plestenjak}, ETNA, Electron. Trans. Numer. Anal. 29, 81--96 (2008; Zbl 1171.65378) Full Text: EuDML EMIS