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The Differential Correction Algorithm

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Delay Equations, Approximation and Application

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Abstract

With the advent of high-speed digital computers came an interest in methods of computing algebraic rational uniform approximations. A major incentive for this interest was the need of computer subroutines for the evaluation of the elementary functions [2, 3, 17, 27, 46]. These approximations continue to have significant applications in the approximation of data sets and complicated mathematical functions. In fact, for one-dimensional data sets, the general concensus is that one should use either a piecewise polynomial fit or a rational fit. In view of this and because of interest in the problem itself many researchers have studied the problem of computation of rational fits. At present two algorithms are generally viewed as being the most effective. They are the Remes algorithm [26, 47, 48, 50] and the differential correction algorithm [4, 14, 15].

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Authors and Affiliations

  1. Department of Mathematics, Colorado State University, 80523, Fort Collins, Colorado, USA

    G. D. Taylor

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  1. G. D. Taylor
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  1. Lehrstuhl für Mathematik IV, Universität Mannheim, D-6800, Mannheim 1, Germany

    G. Meinardus

  2. Fakultät für Mathematik und Informatik, Universität Mannheim, D-6800, Mannheim, Germany

    G. Nürnberger

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© 1985 Birkhäuser Verlag Basel

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Taylor, G.D. (1985). The Differential Correction Algorithm. In: Meinardus, G., Nürnberger, G. (eds) Delay Equations, Approximation and Application. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 74. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7376-5_17

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  • DOI: https://doi.org/10.1007/978-3-0348-7376-5_17

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7378-9

  • Online ISBN: 978-3-0348-7376-5

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