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SIAMMAX
2010

On the Convergence of Rational Ritz Values

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On the Convergence of Rational Ritz Values
Ruhe's rational Krylov method is a popular tool for approximating eigenvalues of a given matrix, though its convergence behavior is far from being fully understood. Under fairly general assumptions we characterize in an asymptotic sense which eigenvalues of a Hermitian matrix are approximated by rational Ritz values and how fast this approximation takes place. Our main tool is a constrained extremal problem from logarithmic potential theory, where an additional external field is required for taking into account the poles of the underlying rational Krylov space. Several examples illustrate our analytic results. Key words. Rational Krylov, Ritz values, orthogonal rational functions, logarithmic potential theory. AMS subject classifications. 15A18, 31A05, 31A15, 65F15
Bernhard Beckermann, Stefan Güttel, Raf Vande
Added 21 May 2011
Updated 21 May 2011
Type Journal
Year 2010
Where SIAMMAX
Authors Bernhard Beckermann, Stefan Güttel, Raf Vandebril
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