Efficient transformation of certain singular polynomial matrix eigenvalue problems

Arne J. Pearlstein, Dimitrios A. Goussis

Research output: Contribution to journalArticlepeer-review


Several transformations of the singular (|Ar| =0) n x n polynomial matrix eigenvalue problem (Arλr+Ar-1λr-1 + ...+A1λ+A0)x = 0 of degree r, where Ar has k<n nonzero rows, are described. The transformed problems are either of degree one, order r(n - 1) + k, and usually (in a sense made precise) nonsingular, or of degree r-1, order n + k, and singular. For a wide range of k, n, and r, the transformed problems can be solved more efficiently than the original problem of degree r and order n.

Original languageEnglish (US)
Pages (from-to)305-312
Number of pages8
JournalJournal of Computational Physics
Issue number2
StatePublished - Oct 1988
Externally publishedYes

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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