A new framework for implicit restarting of the Krylov–Schur algorithm |
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| Authors: | Zvonimir Bujanovi? Zlatko Drma? |
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| Affiliation: | 1. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany;2. Department of Mathematics, University of Zagreb, Zagreb, Croatia |
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| Abstract: | This paper introduces a new framework for implicit restarting of the Krylov–Schur algorithm. It is shown that restarting with arbitrary polynomial filter is possible by reassigning some of the eigenvalues of the Rayleigh quotient through a rank‐one correction, implemented using only the elementary transformations (translation and similarity) of the Krylov decomposition. This framework includes the implicitly restarted Arnoldi (IRA) algorithm and the Krylov–Schur algorithm with implicit harmonic restart as special cases. Further, it reveals that the IRA algorithm can be turned into an eigenvalue assignment method. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | eigenvalues eigenvalue assignment Arnoldi algorithm Krylov– Schur algorithm implicit restart polynomial filter QR algorithm Rayleigh quotient Ritz values |
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