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Nonlinear Numerical Methods and Rational Approximation II pp 321–373Cite as

A Survey of Truncation Error Analysis for Padé and Continued Fraction Approximants

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Part of the book series: Mathematics and Its Applications ((MAIA,volume 296))

Abstract

Many important functions\(f\left( z \right)\) of mathematical physics, chemistry, engineering, and statistics are represented by convergent sequences \(\left\{ {fn\left( z \right)} \right\} \) of rational functions that are entries of a (1-point or multipoint) Padé table for \(f\left( z \right)\) In most cases of practicalinterest \(\left\{ {{{f}_{n}}\left( z \right)} \right\} \) is the sequence of approximants of a continued fraction (see, e.g., [1],[37], [45] and references contained therein). One reason for the importance of Padé tables and related continued fractions is that sequences of their approximants may converge in larger regions of the complex plane C than the power series expansion, which may not converge at all. Also the algorithmic character of continued fractions and Padé approximants provides efficient methods for the computation of special functions.

Research asupported in part by the U.S. National Science Foundation under Grants INT-9113400 and DMS-9302584..

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Authors and Affiliations

  1. Department of Mathematics, University of Colorado, Boulder, CO, 80309-0395, USA

    Cathleen Craviotto, William B. Jones & W. J. Thron

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  1. Cathleen Craviotto
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  2. William B. Jones
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  3. W. J. Thron
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  1. Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium

    Annie Cuyt

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Craviotto, C., Jones, W.B., Thron, W.J. (1994). A Survey of Truncation Error Analysis for Padé and Continued Fraction Approximants. In: Cuyt, A. (eds) Nonlinear Numerical Methods and Rational Approximation II. Mathematics and Its Applications, vol 296. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0970-3_27

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  • DOI: https://doi.org/10.1007/978-94-011-0970-3_27

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