Testing algorithms for linear matrix polynomial equations

Three existing numerical procedures for solution of a linear matrix polynomial equation AX+BY=C have been tested, evaluated and compared in experimental manner. Thousands of examples have been computed thus far covering both generic (randomly created) data and ill-conditioned cases (with ´almost common factors´). The most successful method in the triple appears to be the one based on interpolation (PIM). It has been able to handle generic examples with the polynomial matrices A, B up to sizes 20/spl times/20 of degree 5 as well as ill-conditioned cases with 5/spl times/5 matrices of degree 5 suffering with almost common factors different from the precise ones (for which the equation becomes unsolvable) relatively only by 2/sup -30/. The other two methods considered based on elementary operations and state space realization were found to exhibit some drawbacks in their present form.