On the Convergence of Rational Ritz Values | Zendy

Bernhard Beckermann | Zendy; Stefan Güttel | Zendy; Raf Vandebril | Zendy

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On the Convergence of Rational Ritz Values

Author(s) -

Bernhard Beckermann,

Stefan Güttel,

Raf Vandebril

Publication year - 2010

Publication title -

siam journal on matrix analysis and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.268

H-Index - 101

eISSN - 1095-7162

pISSN - 0895-4798

DOI - 10.1137/090755412

Subject(s) - mathematics , hermitian matrix , eigenvalues and eigenvectors , ritz method , convergence (economics) , rational function , positive definite matrix , matrix (chemical analysis) , analytic function , krylov subspace , field (mathematics) , mathematical analysis , logarithm , pure mathematics , linear system , physics , materials science , quantum mechanics , economics , composite material , boundary value problem , economic growth

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.

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