A new application of the extended Euclidean algorithm for matrix padé approximants

AbstractWork on Padé or Padé-type approximants ultimately involves the explicitdetermination of the polynomials forming the numerator and denominator of rational functions. These exist in the literature useful algorithms for constructing the polynomials when the starting coefficients of the given power series are of the ordinary kind. However, when one has the matrix coefficients forthe series, it becomes necessary to extend the procedure taking into account the special nature of the various operations. In this paper we present a new application of the extended Euclidean algorithm in order to obtain the sets of complete matrix Padé approximants. Also, an efficient Pascal procedure for implementation of the algorithm is given. In fact, the resulting algorithm generates the elements in the anti-diagonal of the Padé table. The concepts and constructive steps involved in the procedure are explained in detail and illustrated by a few suitable examples to show (i) how the algorithm works in general and (ii) the usefulness of the entire approach