A recurrence relation for generalized divided differences with respect to ECT-systems |
| |
Authors: | G. Mühlbach |
| |
Affiliation: | 1. Institut für Angewandte Mathematik, Universit?t Hannover, Welfengarten 1, D-30167, Hannover, Germany
|
| |
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. This revised version was published online in August 2006 with corrections to the Cover Date. |
| |
Keywords: | interpolation ECT-systems generalized divided differences 41A05 65D05 |
本文献已被 SpringerLink 等数据库收录! |
|