Interpolation

  • J. Stoer
  • R. Bulirsch
Part of the Texts in Applied Mathematics book series (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.

Keywords

Attenuation Eosine Summing 

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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • J. Stoer
    • 1
  • R. Bulirsch
    • 2
  1. 1.Institut für Angewandte MathematikUniversität WürzburgWürzburgGermany
  2. 2.Institut für MathematikTechnische UniversitätMünchenGermany

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