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The rational Krylov algorithm for nonsymmetric eigenvalue problems. III: Complex shifts for real matrices

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Abstract

A new algorithm for the computation of eigenvalues of a nonsymmetric matrix pencil is described. It is a generalization of the shifted and inverted Lanczos (or Arnoldi) algorithm, in which several shifts are used in one run. It computes an orthogonal basis and a small Hessenberg pencil. The eigensolution of the Hessenberg pencil, gives Ritz approximations to the solution of the original pencil. It is shown how complex shifts can be used to compute a real block Hessenberg pencil to a real matrix pair.

Two applicationx, one coming from an aircraft stability problem and the other from a hydrodynamic bifurcation, have been tested and results are reported.

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Authors and Affiliations

  1. Department of Computing Science, Chalmers Institute of Technology and the University of Göteborg, S-41296, Göteborg, Sweden

    Axel Ruhe

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  1. Axel Ruhe
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Dedicated to Carl-Erik Fröberg on the occasion of his 75th birthday.

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Ruhe, A. The rational Krylov algorithm for nonsymmetric eigenvalue problems. III: Complex shifts for real matrices. BIT 34, 165–176 (1994). https://doi.org/10.1007/BF01935024

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