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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

Rational Expression Spline Function Polynomial Interpolation Interpolation Problem Support Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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