Evaluating the matrix polynomial I+A+. . .+A N-1

A practical algorithm is described for the evaluation of the matrix polynomial I+A. . .+A^N-1. The algorithm is based on the prime decomposition of NP, and requires at most 3log₂(N) matrix multiplications. The method is applicable to all square matrices and is designed to minimize matrix additions. Thus, as the number of matrix additions and multiplications is minimized, the evaluation will be more accurate than that achieved by other approaches