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Introduction to Numerical Analysis pp 37–124Cite as

Interpolation

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Part of the book series: Texts in Applied Mathematics ((TAM,volume 12))

Abstract

Consider a family of functions of a single variable x,

$$ \Phi \left( {x;{a_o}, \cdots ,{a_n}} \right), $$

having n + 1 parameters αo, ..., αn whose values characterize the individual functions in this family. The interpolation problem for Φ consists of determining these parameters ai so that for n + 1 given real or complex pairs of numbers (xi, fi), i=0, ..., n, with xi ≠ xk for i ≠ k,

$$ \Phi \left( {{x_i};{a_o}, \cdots ,{a_n}} \right) = {f_i},i = 0, \ldots ,n, $$

holds. We will call the pairs (x i, f i) support points, the locations x i support abscissas, and the values f i support ordinates. Occasionally, the values of derivatives of Φ are also prescribed.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Würzburg, am Hubland, 8700, Würzburg, Germany

    J. Stoer

  2. Institut für Mathematik, Technische Universität, 8000, München, Germany

    R. Bulirsch

Authors
  1. J. Stoer
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  2. R. Bulirsch
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© 1993 Springer Science+Business Media New York

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Stoer, J., Bulirsch, R. (1993). Interpolation. In: Introduction to Numerical Analysis. Texts in Applied Mathematics, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2272-7_2

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  • DOI: https://doi.org/10.1007/978-1-4757-2272-7_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-2274-1

  • Online ISBN: 978-1-4757-2272-7

  • eBook Packages: Springer Book Archive

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