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

verfasst von

G. Mühlbach

Abstract

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.

Organisationseinheit(en)

Institut für Angewandte Mathematik

Typ

Artikel

Journal

Numerische Mathematik

Band

32

Seiten

393-408

Anzahl der Seiten

16

ISSN

0029-599X

Publikationsdatum

12.1979

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Computational Mathematics, Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.1007/BF01401043 (Zugang: Geschlossen)