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

authored by: 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.
Organisation(s): Institute of Applied Mathematics
Type: Article
Journal: Numerische Mathematik
Volume: 32
Pages: 393-408
No. of pages: 16
ISSN: 0029-599X
Publication date: 12.1979
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/BF01401043 (Access: Closed)