Abstract

We present a new set of algorithms for computation of matrix rational interpolants and one-sided matrix greatest common divisors. Examples of these interpolants include Padé approximants, Newton-Padé, Padé-Hermite, simultaneous Padé approximants and more generally M-Padé approximants along with their matrix generalizations. The algorithms are meant for computation in exact arithmetic domains where growth of coefficients in intermediate computations are a central concern. This coefficient growth is avoided by using fraction-free methods. At the same time the methods are fast in the sense that they are at least an order of magnitute faster than existing fraction-free methods for the corresponding problems. The methods make use of linear systems having a special striped Krylov structure.