APPLICATIONS OF MATHEMATICS, Vol. 50, No. 6, pp. 543-554, 2005

Rational Krylov for nonlinear eigenproblems,
an iterative projection method

Elias Jarlebring, Heinrich Voss

E. Jarlebring, Institut Computational Mathematics, TU Braunschweig, Pockelsstr. 14, D-38106 Braunschweig, Germany, e-mail:; H. Voss, Department of Mathematics, Hamburg University of Technology, D-21071 Hamburg, Germany, e-mail:

Abstract: In recent papers Ruhe suggested a rational Krylov method for nonlinear eigenproblems knitting together a secant method for linearizing the nonlinear problem and the Krylov method for the linearized problem. In this note we point out that the method can be understood as an iterative projection method. Similarly to the Arnoldi method the search space is expanded by the direction from residual inverse iteration. Numerical methods demonstrate that the rational Krylov method can be accelerated considerably by replacing an inner iteration by an explicit solver of projected problems.

Keywords: nonlinear eigenvalue problem, rational Krylov method, Arnoldi method, projection method

Classification (MSC 2000): 65F15, 65F50, 35P30

Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at
Subscribers of Springer need to access the articles on their site, which is

[Previous Article] [Next Article] [Contents of This Number] [Contents of Applications of Mathematics]