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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 ik 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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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  1. 1.Institut für Angewandte Mathematik und StatistikUniversität WürzburgWürzburgDeutschland

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