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Numerische Mathematik 1 pp 41–146Cite as

Interpolation

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Zusammenfassung

Gegeben sei eine Funktion einer Variablen x

$$\Phi (x;{a_0},...,{a_n}),$$

die von n + 1 weiteren reellen oder komplexen Parametern a 0,..., a n abhängt. Ein Interpolationsproblem für Φ liegt dann vor, wenn die Parameter a i so bestimmt werden sollen, daß für n + 1 gegebene Paare von reellen oder komplexen Zahlen (x i , f i ), i = 0, ..., n, mit x i ≠ x k für i ≠ k gilt

$$\Phi ({x_i};{a_0},...,{a_n}) = {f_i},i = 0,...,n.$$

Die Paare (x i , f i ) werden als Stützpunkte bezeichnet; die x i heißen Stützabszissen, die f i Stützordinaten. Manchmal werden auch Werte der Ableitungen von Φ an den Stützabszissen x i vorgeschrieben.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Am Hubland, D-97074, Würzburg, Deutschland

    Prof. Dr. Josef Stoer

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  1. Prof. Dr. Josef Stoer
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© 1999 Springer-Verlag Berlin Heidelberg

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Stoer, J. (1999). Interpolation. In: Numerische Mathematik 1. Springer-Lehrbuch. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09021-3_2

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  • DOI: https://doi.org/10.1007/978-3-662-09021-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66154-2

  • Online ISBN: 978-3-662-09021-3

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