A recursive algorithm for matrix Padé approximants-the divide-and-conquer approach

In this paper, we present a recursive algorithm for the construction of general matrix Padé approximants. The two main algorithms involved here are MAPORES (MAtrix POlynomial REmainder Sequence), which is a recursive one, and MAPADAC (MAtrix Padé Approximants by Divide-And-Conquer). MAPADAC is based on the divide-and-conquer version of an earlier work on matrix Padé extended Euclidean algorithm (MAPEA). The algorithm is also capable of computing the Padé approximants for the abnormal power series possessing matrix coefficients. An efficient Pascal procedure for implementation of the same is provided here. The different steps involved in the entire approach are explained in detail and illustrated by a few explicit examples. © 1989.