Details
| Original language | English |
|---|---|
| Pages (from-to) | 329-344 |
| Number of pages | 16 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 17 |
| Issue number | 3 |
| Publication status | Published - Mar 1987 |
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.
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of Computational and Applied Mathematics, Vol. 17, No. 3, 03.1987, p. 329-344.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Linear extrapolation by rational functions, exponentials and logarithmic functions
AU - Mühlbach, G.
AU - Reimers, L.
PY - 1987/3
Y1 - 1987/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0023311309&partnerID=8YFLogxK
U2 - 10.1016/0377-0427(87)90109-9
DO - 10.1016/0377-0427(87)90109-9
M3 - Article
AN - SCOPUS:0023311309
VL - 17
SP - 329
EP - 344
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 3
ER -