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Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem. (English) Zbl 1171.65378
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.

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
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