A minimum residual algorithm for solving linear systems |
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| Authors: | Marko Huhtanen Olavi Nevanlinna |
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| Affiliation: | (1) Institute of Mathematics, Helsinki University of Technology, Box 1100, FIN-02015 Helsinki, Finland;(2) Institute of Mathematics, Helsinki University of Technology, Box 1100, FIN-02015 Helsinki, Finland |
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| Abstract: | A minimum residual algorithm for solving a large linear system (I+S)x=b, with b∈ℂ n and S∈ℂ n×n being readily invertible, is proposed. For this purpose Krylov subspaces are generated by applying S and S -1 cyclically. The iteration can be executed with every linear system once the coefficient matrix has been split into the sum of two readily invertible matrices. In case S is a translation and a rotation of a Hermitian matrix, a five term recurrence is devised. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65F10 |
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| Keywords: | minimum residual algorithm Krylov subspace splitting orthogonal rational functions ADI iteration |
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