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The general recurrence relation for divided differences and the general Newton-interpolation-algorithm with applications to trigonometric interpolation

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Summary

In this note an ultimate generalization of Newton's classical interpolation formula is given. More precisely, we will establish the most general linear form of a Newton-like interpolation formula and a general recurrence relation for divided differences which are applicable whenever a function is to be interpolated by means of linear combinations of functions forming a Čebyšev-system such that at least one of its subsystems is again a Čebyšev-system. The theory is applied to trigonometric interpolation yielding a new algorithm which computes the interpolating trigonometric polynomial of smallest degree for any distribution of the knots by recurrence. A numerical example is given.

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Authors and Affiliations

  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 recurrence relation for divided differences and the general Newton-interpolation-algorithm with applications to trigonometric interpolation. Numer. Math. 32, 393–408 (1979). https://doi.org/10.1007/BF01401043

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  • DOI: https://doi.org/10.1007/BF01401043

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