On the computation of determinants arising in some bivariate rational interpolation problems. (English) Zbl 0679.65003
Some results of G. Mühlbach and L. Reimers [J. Comput. Appl. Math. 17, 329-344 (1987; Zbl 0627.65002)], concerning bivariate rational interpolation problems, are extended and the solution to the interpolation problem is obtained in Newton form.
Reviewer: V.Mehrmann
MSC:
| 65D05 | Numerical interpolation |
| 65F40 | Numerical computation of determinants |
| 41A20 | Approximation by rational functions |
| 41A63 | Multidimensional problems |
Citations:
Zbl 0627.65002References:
| [1] | Gasca, M.; Maeztu, J. I., On Lagrange and Hermite interpolation in ℝ \(^k\), Numer. Math., 39, 1-14 (1982) · Zbl 0457.65004 |
| [2] | Gasca, M.; Martínez, J. J., On the computation of multivariate confluent Vandermonde determinants and its applications, (Martin, R., The Mathematics of Surfaces II (1987), Oxford U.P) · Zbl 0643.41003 |
| [3] | Mülbach, G.; Reimers, L., Linear extrapolation by rational functions, exponentials and logarithmic functions, J. Comput. Appl. Math., 17, 329-344 (1987) · Zbl 0627.65002 |
| [4] | Werner, H., Remarks on Newton type multivariate interpolation for subsets of grids, Computing, 25, 181-191 (1980) · Zbl 0419.65005 |
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