Algorithm 766: Experiments with a weakly stable algorithm for computing Padé-Hermite and simultaneous Padé approximants In a recent paper, S. Cabay, A. R. Jones and G. Labahn [SIAM J. Matrix Anal. Appl. 17, No. 2, 248-267, 268-297 (1996; Zbl 0853.65015, Zbl 0853.65016)] 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 [loc. cit.] reflect the general behavior of the actual error, but that in practice these bounds are large overestimates.
(Source: http://dl.acm.org/)

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