Algorithm 766: Experiments with a Weakly Stable Algorithm for Computing PadéHermite and Simultaneous Padé Approximants

Abstract

In a recent paper, Cabay, Jones, and Labahn develop a fast, iterative, lookahead algorithm for numerically computing Padé-Hermite systems and simultaneous Padé systems along a diagonal of the associated Padé tables. Included in their work is a detailed error analysis showing that the algorithm is weakly stable. In this article, we describe a Fortran implementation, VECTOR_PADE, of this algorithm together with a number of numerical experiments. These experiments show that the theoretical error bounds obtained by Cabay, Jones, and Labahn reflect the general behavior of the actual error, but that in practice these bounds are large overestimates.