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The general Neville-Aitken-algorithm and some applications

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In this note we will present the most general linear form of a Neville-Aitken-algorithm for interpolation of functions by linear combinations of functions forming a Čebyšev-system. Some applications are given. Expecially we will give simple new proofs of the recurrence formula for generalized divided differences [5] and of the author's generalization of the classical Neville-Aitkena-algorithm[8]applying to complete Čebyšev-systems. Another application of the general Neville-Aitken-algorithm deals with systems of linear equations. Also a numerical example is given.

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  1. Institut für Praktische Mathematik der Technischen Universität, Welfengarten 1, D-3000, Hannover, Germany (Fed. Rep.)

    G. Mühlbach

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  1. G. Mühlbach
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Mühlbach, G. The general Neville-Aitken-algorithm and some applications. Numer. Math. 31, 97–110 (1978). https://doi.org/10.1007/BF01396017

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