Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 317-326 |
| Seitenumfang | 10 |
| Fachzeitschrift | Numerical algorithms |
| Jahrgang | 22 |
| Ausgabenummer | 3-4 |
| Publikationsstatus | Veröffentlicht - Feb. 1999 |
Abstract
It is well known that ordinary divided differences can be computed recursively. This holds true also for generalized divided differences with respect to complete Chebyshev-systems. In this note for extended complete Chebyshev-systems and possibly repeated nodes for the recurrence relation a simple proof is given which also covers the case of complex valued functions. As an application, interpolation by linear combinations of certain complex exponential functions is considered. Moreover, it is shown that generalized divided differences are also continuous functions of their nodes.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Angewandte Mathematik
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in: Numerical algorithms, Jahrgang 22, Nr. 3-4, 02.1999, S. 317-326.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - A recurrence relation for generalized divided differences with respect to ECT-systems
AU - Mühlbach, G.
PY - 1999/2
Y1 - 1999/2
N2 - It is well known that ordinary divided differences can be computed recursively. This holds true also for generalized divided differences with respect to complete Chebyshev-systems. In this note for extended complete Chebyshev-systems and possibly repeated nodes for the recurrence relation a simple proof is given which also covers the case of complex valued functions. As an application, interpolation by linear combinations of certain complex exponential functions is considered. Moreover, it is shown that generalized divided differences are also continuous functions of their nodes.
AB - It is well known that ordinary divided differences can be computed recursively. This holds true also for generalized divided differences with respect to complete Chebyshev-systems. In this note for extended complete Chebyshev-systems and possibly repeated nodes for the recurrence relation a simple proof is given which also covers the case of complex valued functions. As an application, interpolation by linear combinations of certain complex exponential functions is considered. Moreover, it is shown that generalized divided differences are also continuous functions of their nodes.
KW - ECT-systems
KW - Generalized divided differences
KW - Interpolation
UR - http://www.scopus.com/inward/record.url?scp=0042078467&partnerID=8YFLogxK
U2 - 10.1023/a:1019175311651
DO - 10.1023/a:1019175311651
M3 - Article
AN - SCOPUS:0042078467
VL - 22
SP - 317
EP - 326
JO - Numerical algorithms
JF - Numerical algorithms
SN - 1017-1398
IS - 3-4
ER -