An iterated shift-and-invert Arnoldi algorithm for quadratic matrix eigenvalue problems

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6 Scopus citations

Abstract

For solving the large scale quadratic eigenvalue problem L(λ)x: = (Aλ2 + Bλ + C)x = 0, a direct projection method based on the Krylov subspaces generated by a single matrix A-1B using the standard Arnoldi algorithm is considered. It is shown that, when iteratively combined with the shift-and-invert technique, it results in a fast converging algorithm. The important situations of inexact shift-and-invert are also discussed and numerical examples are presented to illustrate the new method.

Original languageEnglish
Pages (from-to)818-827
Number of pages10
JournalApplied Mathematics and Computation
Volume172
Issue number2 SPEC. ISS.
DOIs
StatePublished - Jan 15 2006

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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