Details
| Original language | English |
|---|---|
| Pages (from-to) | 297-309 |
| Number of pages | 13 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 26 |
| Issue number | 3 |
| Publication status | Published - Jul 1989 |
Abstract
A constructive proof for existence and unicity of the rational RM,N belonging to RM,N, M ≥ 0, N ≥ 0, having prescribed N poles and interpolating M + 1 Hermite data is given. It is based upon explicit computation of the confluent Cauchy-Vandermonde determinant in terms of the nodes and the poles. An algorithm to compute RM,N(z) is presented. It calculates this value from a triangular field of values of rational interpolants of lowest possible orders. The algorithm is based upon a Neville-Aitken interpolation formula and has arithmetical complexity O(L2), L{colon equals} max(M + 1, N).
Keywords
- Interpolation, prescribed poles, rational functions
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of Computational and Applied Mathematics, Vol. 26, No. 3, 07.1989, p. 297-309.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Computation of rational interpolants with prescribed poles
AU - Gasca, M.
AU - Martínez, J. J.
AU - Mühlbach, G.
PY - 1989/7
Y1 - 1989/7
N2 - A constructive proof for existence and unicity of the rational RM,N belonging to RM,N, M ≥ 0, N ≥ 0, having prescribed N poles and interpolating M + 1 Hermite data is given. It is based upon explicit computation of the confluent Cauchy-Vandermonde determinant in terms of the nodes and the poles. An algorithm to compute RM,N(z) is presented. It calculates this value from a triangular field of values of rational interpolants of lowest possible orders. The algorithm is based upon a Neville-Aitken interpolation formula and has arithmetical complexity O(L2), L{colon equals} max(M + 1, N).
AB - A constructive proof for existence and unicity of the rational RM,N belonging to RM,N, M ≥ 0, N ≥ 0, having prescribed N poles and interpolating M + 1 Hermite data is given. It is based upon explicit computation of the confluent Cauchy-Vandermonde determinant in terms of the nodes and the poles. An algorithm to compute RM,N(z) is presented. It calculates this value from a triangular field of values of rational interpolants of lowest possible orders. The algorithm is based upon a Neville-Aitken interpolation formula and has arithmetical complexity O(L2), L{colon equals} max(M + 1, N).
KW - Interpolation
KW - prescribed poles
KW - rational functions
UR - http://www.scopus.com/inward/record.url?scp=38249023439&partnerID=8YFLogxK
U2 - 10.1016/0377-0427(89)90302-6
DO - 10.1016/0377-0427(89)90302-6
M3 - Article
AN - SCOPUS:38249023439
VL - 26
SP - 297
EP - 309
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 3
ER -