A new extension of Leverrier's algorithm

Abstract An algorithm for computing the inverse of a matrix polynomial s N J - s N -1A 1 -⋯- sA N-1 - A N is given, where J is a singular matrix. This algorithm is a new extension of Leverrier's algorithm for computing the inverse of a matrix polynomial s N I - s N -1 A 1 -⋯- sA N -1- A N , where I denotes the unit matrix.