Numerical algorithms for polynomial plus/minus factorization

• Published in: International journal of robust and nonlinear control Vol. 17; no. 8; pp. 786 - 802
• Main Authors: Hromcik, M, Sebek, M
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 25.05.2007
• Subjects: numerical algorithms; polynomial design methods; polynomial factorizations
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.1132

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 H2‐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 l1 optimal controller design example. Copyright © 2006 John Wiley & Sons, Ltd.