A note on the evaluation of matrix polynomials
Charles F. Van Loan · IEEE Transactions on Automatic Control · 1979
The problem of evaluating a polynomialp(x)in a matrixAarises in many applications, e.g., the Taylor approximation of eA. The0(\sqrt{q} n^{3})algorithm of Paterson and Stockmeyer has the drawback that it requires0(\sqrt{q}q n^{2})storage, whereqis the degree ofpandnis the dimension ofA. An algorithm which greatly reduces this storage requirement without undue loss of speed is presented.