Two-sided harmonic subspace extractions for the generalized eigenvalue problem |
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Authors: | Peter Benner Michiel Hochstenbach Patrick Kürschner |
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Institution: | 1. Max Planck Institute for Dynamics of Complex Technical Systems: Computational Methods in Systems and Control Theory, Sandtorstr. 1, 39106 Magdeburg;2. Technische Universiteit Eindhoven: Centre for Analysis, Scientific Computing and Applications, Den Dolech 2, NL-5612 AZ Eindhoven |
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Abstract: | 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. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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