Linear extrapolation by rational functions,exponentials and logarithmic functions |
| |
Affiliation: | Institut für Angewandte Mathematik, Universität Hannover, D-3000 Hannover 1, Germany |
| |
Abstract: | In this paper linear extrapolation by rational functions with given poles is considered from an arithmetical point of view. It is shown that the classical interpolation algorithms of Lagrange, Neville-Aitken and Newton which are well known for polynomial interpolation can be extended in a natural way to this problem yielding recursive methods of nearly the same complexity. The proofs are based upon explicit representations of generalized Vandermonde-determinants which are calculated by the elimination method combined with analytical considerations. As an application a regularity criterion for certain linear sequence-transformations is given. Also, by the same method simplified recurrence relations for linear extrapolation by exponentials and logarithmic functions at special knots are derived. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|