Using implicitly ltered RKS for generalised eigenvalue problems
نویسندگان
چکیده
The rational Krylov sequence (RKS) method can be seen as a generalisation of Arnoldi’s method. It projects a matrix pencil onto a smaller subspace; this projection results in a small upper Hessenberg pencil. As for the Arnoldi method, RKS can be restarted implicitly, using the QR decomposition of a Hessenberg matrix. This restart comes with a projection of the subspace using a rational function. In this paper, it is shown how the restart can be worked out in practice. In a second part, it is shown when the ltering of the subspace basis can fail and how this failure can be handled by de ating a converged eigenvector from the subspace, using a Schur-decomposition. c © 1999 Elsevier Science B.V. All rights reserved.
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Using Implicitly Filtered RKS for generalised eigenvalue problems
The Rational Krylov Sequence (RKS) method can be seen as a generalisation of Arnoldi's method. It projects a matrix pencil onto a smaller subspace; this projection results in a small upper Hessenberg pencil. As for the Arnoldi method, RKS can be restarted implicitly, using the QR decomposition of a Hessenberg matrix. This restart comes with a projection of the subspace using a rational function...
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