EFFICIENT NUMERICAL-METHOD FOR THE DISCRETE-TIME SYMMETRICAL MATRIX POLYNOMIAL EQUATION

A numerical procedure is proposed to solve a matrix polynomial equatio n frequently encountered in discrete-time control and signal processin g. The algorithm is based on a simple rewriting of the original equati on in terms of a reduced Sylvester matrix. In contrast to previously p ublished methods, it does not make use of elementary polynomial operat ions. Moreover, and most notably, it is numerically reliable. Basic ex amples borrowed from control and signal processing literature are aime d at illustrating the simplicity and efficiency of this new numerical method.