Details
| Original language | English |
|---|---|
| Pages (from-to) | 203-222 |
| Number of pages | 20 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 122 |
| Issue number | 1 |
| Early online date | 25 Sept 2000 |
| Publication status | Published - 1 Oct 2000 |
Abstract
Cauchy-Vandermonde systems consist of rational functions with prescribed poles. They are complex ECT-systems allowing Hermite interpolation for any dimension of the basic space. A survey of interpolation procedures using CV-systems is given, some equipped with short new proofs, which generalize the well-known formulas of Lagrange, Neville-Aitken and Newton for interpolation by algebraic polynomials. The arithmetical complexitiy is O(N2) for N Hermite data. Also, inversion formulas for the Cauchy-Vandermonde matrix are surveyed. Moreover, a new algorithm solving the system of N linear Cauchy-Vandermonde equations for multiple nodes and multiple poles recursively is given which does not require additional partial fraction decompositions. As an application construction of rational B-splines with prescribed poles is discussed.
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of Computational and Applied Mathematics, Vol. 122, No. 1, 01.10.2000, p. 203-222.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Interpolation by Cauchy-Vandermonde systems and applications
AU - Mühlbach, G.
PY - 2000/10/1
Y1 - 2000/10/1
N2 - Cauchy-Vandermonde systems consist of rational functions with prescribed poles. They are complex ECT-systems allowing Hermite interpolation for any dimension of the basic space. A survey of interpolation procedures using CV-systems is given, some equipped with short new proofs, which generalize the well-known formulas of Lagrange, Neville-Aitken and Newton for interpolation by algebraic polynomials. The arithmetical complexitiy is O(N2) for N Hermite data. Also, inversion formulas for the Cauchy-Vandermonde matrix are surveyed. Moreover, a new algorithm solving the system of N linear Cauchy-Vandermonde equations for multiple nodes and multiple poles recursively is given which does not require additional partial fraction decompositions. As an application construction of rational B-splines with prescribed poles is discussed.
AB - Cauchy-Vandermonde systems consist of rational functions with prescribed poles. They are complex ECT-systems allowing Hermite interpolation for any dimension of the basic space. A survey of interpolation procedures using CV-systems is given, some equipped with short new proofs, which generalize the well-known formulas of Lagrange, Neville-Aitken and Newton for interpolation by algebraic polynomials. The arithmetical complexitiy is O(N2) for N Hermite data. Also, inversion formulas for the Cauchy-Vandermonde matrix are surveyed. Moreover, a new algorithm solving the system of N linear Cauchy-Vandermonde equations for multiple nodes and multiple poles recursively is given which does not require additional partial fraction decompositions. As an application construction of rational B-splines with prescribed poles is discussed.
UR - http://www.scopus.com/inward/record.url?scp=0034289785&partnerID=8YFLogxK
U2 - 10.1016/S0377-0427(00)00364-2
DO - 10.1016/S0377-0427(00)00364-2
M3 - Article
AN - SCOPUS:0034289785
VL - 122
SP - 203
EP - 222
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 1
ER -