On the convergence of rational ritz values

Bernhard Beckermann, Stefan Güttel, Raf Vandebril

    Research output: Contribution to journalArticlepeer-review


    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. Copyright © 2010 Society for Industrial and Applied Mathematics.
    Original languageEnglish
    Pages (from-to)1740-1774
    Number of pages34
    JournalSIAM Journal on Matrix Analysis and Applications
    Issue number4
    Publication statusPublished - 2009


    • Logarithmic potential theory
    • Orthogonal rational functions
    • Rational Krylov
    • Ritz values


    Dive into the research topics of 'On the convergence of rational ritz values'. Together they form a unique fingerprint.

    Cite this