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Numerical algorithms for polynomial plus/minus factorization
Author(s) -
Hromčík M.,
Šebek M.
Publication year - 2006
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1132
Subject(s) - factorization , toeplitz matrix , discrete fourier transform (general) , scalar (mathematics) , factorization of polynomials , polynomial , algorithm , inverse , dixon's factorization method , fast fourier transform , mathematics , matrix decomposition , nyquist–shannon sampling theorem , fourier transform , cyclotomic fast fourier transform , discrete sine transform , matrix polynomial , fourier analysis , pure mathematics , fractional fourier transform , mathematical analysis , geometry , eigenvalues and eigenvectors , quantum mechanics , physics
Abstract Two new algorithms are presented in the paper for the plus/minus factorization of a scalar discrete‐time polynomial. The first method is based on the discrete Fourier transform theory (DFT) and its relationship to the Z‐transform. Involving DFT computational techniques and the famous fast Fourier transform routine brings high computational efficiency and reliability. The method is applied in the case study of H 2 ‐optimal inverse dynamic filter to an audio equipment. The second numerical procedure originates in a symmetric spectral factorization routine, namely the Bauer's method of the 1950s. As a by‐product, a recursive LU factorization procedure for Toeplitz matrices is devised that is of more general impact and can be of use in other areas of applied mathematics as well. Performance of the method is demonstrated by an l 1 optimal controller design example. Copyright © 2006 John Wiley & Sons, Ltd.