Hochstenbach, Michiel E.; Kosir, Tomaz; Plestenjak, Bor A Jacobi–Davidson type method for the two-parameter eigenvalue problem. (English) Zbl 1077.65036 SIAM J. Matrix Anal. Appl. 26, No. 2, 477-497 (2005). Summary: We present a new numerical method for computing selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. The method does not require good initial approximations and is able to tackle large problems that are too expensive for methods that compute all eigenvalues. The new method uses a two-sided approach and is a generalization of the Jacobi-Davidson type method for right definite two-parameter eigenvalue problems [cf. M. E. Hochstenbach and B. Plestenjak, SIAM J. Matrix Anal. Appl. 24, No. 2, 392–410 (2002; Zbl 1025.65023)]. Here we consider the much wider class of nonsingular problems. In each step we first compute Petrov triples of a small projected two-parameter eigenvalue problem and then expand the left and right search spaces using approximate solutions to appropriate correction equations. Using a selection technique, it is possible to compute more than one eigenpair. Some numerical examples are presented. Cited in 30 Documents MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices Keywords:two-parameter eigenvalue problem; subspace method; Jacobi-Davidson method; correction equation; Petrov-Galerkin; two-sided approach; numerical examples Citations:Zbl 1025.65023 Software:JDQZ; JDQR PDFBibTeX XMLCite \textit{M. E. Hochstenbach} et al., SIAM J. Matrix Anal. Appl. 26, No. 2, 477--497 (2005; Zbl 1077.65036) Full Text: DOI