An exploratory study of a subspace iteration method as an alternative to the QR method for Floquet eigenanalysis

  • Authors:

  • N. S. Achar;G. H. Gaonkar

  • Affiliations:

  • Florida Atlantic University Boca Raton, FL 33431, U.S.A.;Florida Atlantic University Boca Raton, FL 33431, U.S.A.

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 1994

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Abstract

Floquet eigenanalysis requires a few dominant eigenvalues of the Floquet transition matrix (FTM). Although the QR method is used almost exclusively, it is expensive for such partial eigenanalysis; the operation counts and, thereby, the approximate machine-time grow cubically with the matrix order. Accordingly, for Floquet eigenanalysis, the Arnoldi-Saad method, a subspace iteration method, is investigated as an alternative to the QR method. The two methods are compared for machine-time efficiency and computational reliability, which is quantified by the condition numbers of the required eigenvalues and the residual errors of the corresponding eigenpairs. The Arnoldi-Saad method takes much less machine-time than the QR method with comparable computational reliability and offers promise for large-scale Floquet eigenanalysis (say, FTM order 100).