Iterative refinement techniques for the spectral factorization of polynomials

A. Bacciardi; Luca Gemignani

doi:10.1117/12.452468

6 December 2002 Iterative refinement techniques for the spectral factorization of polynomials

A. Bacciardi, Luca Gemignani

Proceedings Volume 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII; (2002) https://doi.org/10.1117/12.452468
Event: International Symposium on Optical Science and Technology, 2002, Seattle, WA, United States

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.

Citation Download Citation

A. Bacciardi and Luca Gemignani "Iterative refinement techniques for the spectral factorization of polynomials", Proc. SPIE 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII, (6 December 2002); https://doi.org/10.1117/12.452468

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