Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 393-408 |
| Seitenumfang | 16 |
| Fachzeitschrift | Numerische Mathematik |
| Jahrgang | 32 |
| Ausgabenummer | 4 |
| Publikationsstatus | Veröffentlicht - Dez. 1979 |
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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: Numerische Mathematik, Jahrgang 32, Nr. 4, 12.1979, S. 393-408.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - The general recurrence relation for divided differences and the general Newton-interpolation-algorithm with applications to trigonometric interpolation
AU - Mühlbach, G.
PY - 1979/12
Y1 - 1979/12
N2 - 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.
AB - 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.
KW - Subject Classifications: AMS(MOS), 65D05, 41A05, 42A12
UR - http://www.scopus.com/inward/record.url?scp=4243486428&partnerID=8YFLogxK
U2 - 10.1007/BF01401043
DO - 10.1007/BF01401043
M3 - Article
AN - SCOPUS:4243486428
VL - 32
SP - 393
EP - 408
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 4
ER -