Reliable Algorithms for Polynomial Matrices

A unified approach is pursued for designing efficient and numerically reliable algorithms for polynomial matrices. Based on two standard polynomial techniques -- Sylvester matrices and interpolation -- several algorithms are developed for performing fundamental operations such as polynomial matrix rank evaluation, polynomial matrix triangularization (as a special case of greatest common divisor extraction) and resolution of bilateral symmetric matrix polynomial equations arising in continuous- and discrete-time spectral factorization. Relevant features of this unified approach are efficiency and reliability, as illustrated by numerical experiments. The algorithms were implemented and tested as a part of the Polynomial Toolbox for Matlab. Anotace Pr'ace prin'as'i jednotn'y pr'istup k n'avrhu ' ucinn'ych a numericky spolehliv'ych algoritmu pro polynomi'aln'i matice. Na z'aklade standardn'ich polynomi'aln'ich technik -- Sylvestrovy matice a interpolace -- je odvozeno nekolik nov'ych algor..