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TW 565

Karl Meerbergen and Raf Vandebril
A reflection on the implicitly restarted Arnoldi method for computing eigenvalues near a vertical line

Abstract

In this article, we will study the link between a method for computing eigenvalues closest to the imaginary axis and the implicitly restarted Arnoldi method. In a recent publication Meerbergen and Spence discussed a new approach for detecting purely imaginary eigenvalues corresponding to Hopf bifurcations. The proposed method is based on inverse iteration on a Lyapunov like eigenvalue problem. A projection step was added that significantly reduces the computational overhead. The same method can be used for computing eigenvalues of a matrix near a vertical line in the complex plane. This method then appears to be equivalent with the implicitly restarted Arnoldi method by Sorensen with a special choice of shifts.

report.pdf (165K) / mailto: K. Meerbergen