An algorithm for inverting polynomial matrices

Abstract

Abstract This paper gives an algorithm for computing the inverses of polynomial matrices. The Gauss-Jordan inversion method, which is commonly used for the numerical inversion of constant matrices, can be applied to the inversion of polynomial matrices. It requires, however, operations with polynomials. Moreover, in the division of the operations, if the common factors in the divisor polynomials and the dividend polynomials are not eliminated, the resultant inverse contains polynomials of high degree in the numerators and the denominators. An algorithm given in this paper requires only operations with constant matrices. This algorithm gives an inverse in the minimal degree form if a polynomial matrix to be inverted is not a special form. It is shown that this is faster than existing ones. Also, it is an extension of the Souriau-Frame-Faddeev one. Some examples are illustrated to show the feasibility of the algorithm.