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Proceedings Paper

Iterative refinement techniques for the spectral factorization of polynomials
Author(s): A. Bacciardi; Luca Gemignani
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Paper Abstract

In this paper we propose a superfast implementation of Wilson's method for the spectral factorization of Laurent polynomials based on a preconditioned conjugate gradient algorithm. The new computational scheme follows by exploiting several recently established connections between the considered factorization problem and the solution of certain discrete-time Lyapunov matrix equations whose coefficients are in controllable canonical form. The results of many numerical experiments even involving polynomials of very high degree are reported and discussed by showing that our preconditioning strategy is quite effective just when starting the iterative phase with a roughly approximation of the sought factor. Thus, our approach provides an efficient refinement procedure which is particularly suited to be combined with linearly convergent factorization algorithms when suffering from a very slow convergence due to the occurrence of roots close to the unit circle.

Paper Details

Date Published: 6 December 2002
PDF: 12 pages
Proc. SPIE 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII, (6 December 2002); doi: 10.1117/12.452468
Show Author Affiliations
A. Bacciardi, Univ. degli Studi di Pisa (Italy)
Luca Gemignani, Univ. degli Studi di Pisa (Italy)


Published in SPIE Proceedings Vol. 4791:
Advanced Signal Processing Algorithms, Architectures, and Implementations XII
Franklin T. Luk, Editor(s)

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