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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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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DOI: https://doi.org/10.1007/BF01935024