Two-sided harmonic subspace extractions for the generalized eigenvalue problem

P. Benner, M.E. Hochstenbach, P. Kürschner

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


One crucial step of the solution of large-scale generalized eigenvalue problems with iterative subspace methods, e.g. Arnoldi, Jacobi-Davidson, is a projection of the original large-scale problem onto a low dimensional subspaces. Here we investigate two-sided methods, where approximate eigenvalues together with their right and left eigenvectors of the full-size problem are extracted from the resulting small eigenproblem. The two-sided Ritz-Galerkin projection can be seen as the most basic form of this approach. It usually provides a good convergence towards the extremal eigenvalues of the spectrum. For improving the convergence towards interior eigenvalues, we investigate two approaches based on harmonic subspace extractions for the generalized eigenvalue problem.
Original languageEnglish
Title of host publicationProceedings 82th Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik e.V. (GAMM 2011, Graz, Austria, April 18-22, 2011)
Publication statusPublished - 2012

Publication series

NamePAMM, Proceedings in Applied Mathematics and Mechanics
ISSN (Print)1617-7061


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