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Advances in Computational Mathematics

, Volume 7, Issue 4, pp 429–454 | Cite as

Spectral factorization of Laurent polynomials

  • Tim N.T. Goodman
  • Charles A. Micchelli
  • Giuseppe Rodriguez
  • Sebastiano Seatzu
Article

Abstract

We analyse the performance of five numerical methods for factoring a Laurent polynomial, which is positive on the unit circle, as the modulus squared of a real algebraic polynomial. It is found that there is a wide disparity between the methods, and all but one of the methods are significantly influenced by the variation in magnitude of the coefficients of the Laurent polynomial, by the closeness of the zeros of this polynomial to the unit circle, and by the spacing of these zeros.

spectral factorization Toeplitz matrices Euler–Frobenius polynomials Daubechies wavelets 12D05 15A23 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Tim N.T. Goodman
    • 1
  • Charles A. Micchelli
    • 2
  • Giuseppe Rodriguez
    • 3
  • Sebastiano Seatzu
    • 3
  1. 1.Department of Mathematical SciencesUniversity of DundeeDundeeUK
  2. 2.IBM Research Division, T.J. Watson Research CenterYorktown HeightsUSA
  3. 3.Department of MathematicsUniversity of CagliariCagliariItaly

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