## Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems.(English)Zbl 0539.65013

Iterative algorithms for lage sparse nonsymmetric eigenvalue problems are considered. A Chebyshev semi-iteration is used to damp out the contributions from the eigenvalues in an ellipse in the complex plane. If the ellipse has foci $$d\pm c$$, where d is real and c is either real or purely imaginary, such an iteration can be performed in real arithmetic. Eigenvalues outside the ellipse are found by the Arnoldi method, or by subspace iteration. It is shown that the Arnoldi-Chebyshev method, where results from Arnoldi are used to update the parameters d and c of the ellipse, is the algorithm to be preferred. Numerical experiments are presented.
Reviewer: A.Ruhe

### MSC:

 65F15 Numerical computation of eigenvalues and eigenvectors of matrices

SRRIT
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