Applications of Mathematics

, Volume 50, Issue 6, pp 543–554 | Cite as

Rational Krylov for Nonlinear Eigenproblems, an Iterative Projection Method

  • Elias Jarlebring
  • Heinrich Voss


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.


nonlinear eigenvalue problem rational Krylov method Arnoldi method projection method 


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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2005

Authors and Affiliations

  • Elias Jarlebring
    • 1
  • Heinrich Voss
    • 2
  1. 1.Institut Computational MathematicsTU BraunschweigBraunschweigGermany
  2. 2.Department of MathematicsHamburg University of TechnologyHamburgGermany

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