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Continued fractions associated with the Newton-Padé table

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Summary

We discuss first the block structure of the Newton-Padé table (or, rational interpolation table) corresponding to the double sequence of rational interpolants for the data{(z k, h(zk)} ∞k =0. (The (m, n)-entry of this table is the rational function of type (m,n) solving the linearized rational interpolation problem on the firstm+n+1 data.) We then construct continued fractions that are associated with either a diagonal or two adjacent diagonals of this Newton-Padé table in such a way that the convergents of the continued fractions are equal to the distinct entries on this diagonal or this pair of diagonals, respectively. The resulting continued fractions are generalizations of Thiele fractions and of Magnus'sP-fractions. A discussion of an some new results on related algorithms of Werner and Graves-Morris and Hopkins are also given.

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  1. Interdisciplinary Project Center for Supercomputing, ETH Zurich, ETH-Zentrum, CH-8092, Zurich

    Martin H. Gutknecht

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  1. Martin H. Gutknecht
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Dedicated to the memory of Helmut Werner (1931–1985)

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Gutknecht, M.H. Continued fractions associated with the Newton-Padé table. Numer. Math. 56, 547–589 (1989). https://doi.org/10.1007/BF01396344

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  • DOI: https://doi.org/10.1007/BF01396344

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