TY - GEN

T1 - Two-sided harmonic subspace extractions for the generalized eigenvalue problem

AU - Benner, P.

AU - Hochstenbach, M.E.

AU - Kürschner, P.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

M3 - Conference contribution

T3 - PAMM, Proceedings in Applied Mathematics and Mechanics

SP - 739

EP - 740

BT - Proceedings 82th Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik e.V. (GAMM 2011, Graz, Austria, April 18-22, 2011)

ER -