engleski

A new framework for implicit restarting of the Krylov-Schur algorithm

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 algorithm (IRA), 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.

Eigenvalues ; eigenvalue assignment ; Arnoldi algorithm ; Krylov-Schur algorithm ; implicit restart ; polynomial filter ; QR algorithm ; Rayleigh quotient ; Ritz values

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