Riccati-based preconditioner for computing invariant subspaces of large matrices |
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Authors: | M Robbé M Sadkane |
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Institution: | (1) Université de Bretagne Occidentale, Département de Mathématiques, 6, Av. Le Gorgeu, BP 809, 29285 Brest Cedex, France; e-mail: {robbe,sadkane}@univ-brest.fr , FR |
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Abstract: | Summary. This paper introduces and analyzes the convergence properties of a method that computes an approximation to the invariant
subspace associated with a group of eigenvalues of a large not necessarily diagonalizable matrix. The method belongs to the
family of projection type methods. At each step, it refines the approximate invariant subspace using a linearized Riccati's
equation which turns out to be the block analogue of the correction used in the Jacobi-Davidson method. The analysis conducted
in this paper shows that the method converges at a rate quasi-quadratic provided that the approximate invariant subspace is
close to the exact one. The implementation of the method based on multigrid techniques is also discussed and numerical experiments
are reported.
Received June 15, 2000 / Revised version received January 22, 2001 / Published online October 17, 2001 |
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Keywords: | Mathematics Subject Classification (1991): 65F15 |
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