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.
|Title of host publication||Proceedings 82th Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik e.V. (GAMM 2011, Graz, Austria, April 18-22, 2011)|
|Publication status||Published - 2012|
|Name||PAMM, Proceedings in Applied Mathematics and Mechanics|