Details
| Original language | English |
|---|---|
| Pages (from-to) | 97-110 |
| Number of pages | 14 |
| Journal | Numerische Mathematik |
| Volume | 31 |
| Issue number | 1 |
| Publication status | Published - Mar 1978 |
Abstract
In this note we will present the most general linear form of a Neville-Aitken-algorithm for interpolation of functions by linear combinations of functions forming a Čebyšev-system. Some applications are given. Expecially we will give simple new proofs of the recurrence formula for generalized divided differences [5] and of the author's generalization of the classical Neville-Aitkena-algorithm[8]applying to complete Čebyšev-systems. Another application of the general Neville-Aitken-algorithm deals with systems of linear equations. Also a numerical example is given.
Keywords
- Subject Classifications: AMS (MOS): 65D05, 65B05, 65F05
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Numerische Mathematik, Vol. 31, No. 1, 03.1978, p. 97-110.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The general Neville-Aitken-algorithm and some applications
AU - Mühlbach, G.
PY - 1978/3
Y1 - 1978/3
N2 - In this note we will present the most general linear form of a Neville-Aitken-algorithm for interpolation of functions by linear combinations of functions forming a Čebyšev-system. Some applications are given. Expecially we will give simple new proofs of the recurrence formula for generalized divided differences [5] and of the author's generalization of the classical Neville-Aitkena-algorithm[8]applying to complete Čebyšev-systems. Another application of the general Neville-Aitken-algorithm deals with systems of linear equations. Also a numerical example is given.
AB - In this note we will present the most general linear form of a Neville-Aitken-algorithm for interpolation of functions by linear combinations of functions forming a Čebyšev-system. Some applications are given. Expecially we will give simple new proofs of the recurrence formula for generalized divided differences [5] and of the author's generalization of the classical Neville-Aitkena-algorithm[8]applying to complete Čebyšev-systems. Another application of the general Neville-Aitken-algorithm deals with systems of linear equations. Also a numerical example is given.
KW - Subject Classifications: AMS (MOS): 65D05, 65B05, 65F05
UR - http://www.scopus.com/inward/record.url?scp=0005432868&partnerID=8YFLogxK
U2 - 10.1007/BF01396017
DO - 10.1007/BF01396017
M3 - Article
AN - SCOPUS:0005432868
VL - 31
SP - 97
EP - 110
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 1
ER -