Rational Krylov for nonlinear eigenproblems, an iterative projection method

Elias Jarlebring; Heinrich Voss

Applications of Mathematics (2005)

  • Volume: 50, Issue: 6, page 543-554
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Jarlebring, Elias, and Voss, Heinrich. "Rational Krylov for nonlinear eigenproblems, an iterative projection method." Applications of Mathematics 50.6 (2005): 543-554. <http://eudml.org/doc/33237>.

@article{Jarlebring2005,
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.},
author = {Jarlebring, Elias, Voss, Heinrich},
journal = {Applications of Mathematics},
keywords = {nonlinear eigenvalue problem; rational Krylov method; Arnoldi method; projection method; nonlinear eigenvalue problem; rational Krylov method; Arnoldi method; projection method},
language = {eng},
number = {6},
pages = {543-554},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Rational Krylov for nonlinear eigenproblems, an iterative projection method},
url = {http://eudml.org/doc/33237},
volume = {50},
year = {2005},
}

TY - JOUR
AU - Jarlebring, Elias
AU - Voss, Heinrich
TI - Rational Krylov for nonlinear eigenproblems, an iterative projection method
JO - Applications of Mathematics
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 6
SP - 543
EP - 554
AB - 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.
LA - eng
KW - nonlinear eigenvalue problem; rational Krylov method; Arnoldi method; projection method; nonlinear eigenvalue problem; rational Krylov method; Arnoldi method; projection method
UR - http://eudml.org/doc/33237
ER -

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