ALGORITHM-766 - EXPERIMENTS WITH A WEAKLY STABLE ALGORITHM FOR COMPUTING PADE-HERMITE AND SIMULTANEOUS PADE APPROXIMANTS

In a recent paper, Cabay, Jones, and Labahn develop a fast, iterative, lookahead algorithm for numerically computing Pade-Hermite systems an d simultaneous Pade systems along a diagonal of the associated Pade ta bles. Included in their work is a detailed error analysis showing that the algorithm is weakly stable. In this article, we describe a Fortra n implementation, VECTOR_PADE, of this algorithm together with a numbe r of numerical experiments. These experiments show that the theoretica l error bounds obtained by Cabay, Jones, and Labahn reflect the genera l behavior of the actual error, but that in practice these bounds are large overestimates.