Experiments with a Weakly Stable Algorithm for Computing Pade'-Hermite and Simultaneous Pade' Approximants

S. Cabay, A. Jones and G. Labahn

Abstract

In a recent paper, the authors have developed a fast, iterative, look-ahead algorithm for numerically computing Pade'-Hermite systems and simultaneous Pade' systems along a diagonal of the associated Pade' tables. Included there is a detailed error analysis showing that the algorithm is weakly stable. In this paper, 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 reflect the general behavior of the actual error, but that in practice these bounds are large over-estimates.

The complete document can be retrieved by anonymous ftp at ftp.cs.ualberta.ca/pub/cabay/experiments_pade_alg.ps.Z

The fortran 77 code for VECTOR_PADE is available by anonymous ftp at ftp.cs.ualberta.ca/pub/cabay/pade_software/vector_pade

[University of Alberta]
University of Alberta 		[Department of Computing Science]
Computing Science 		[Stan Cabay's home page]
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