An efficient numerical method for the discrete time symmetric matrix polynomial equation

A novel numerical procedure is proposed to solve the discrete time symmetric matrix polynomial equation A'(d⁻¹)X(d.) +X'(d⁻¹)A(d) = B(d) frequently encountered in control and signal processing. In contrast to previously published methods, it does not make use of elementary polynomial operations. The algorithm is based on a simple rewriting of the original equation in terms of reduced Sylvester resultant matrices. It handles all critical cases and namely, is numerically reliable. Some basic examples are provided to illustrate the simplicity and efficiency of the numerical method.