Polynomial interpolation on interlacingrectangular grids. (English) Zbl 1373.65010
Summary: In this paper we establish the unisolvence of any interlacing pair of rectangular grids of points with respect to a large class of associated polynomial spaces. This includes interpolation on Padua points and the schemes of C. R. Morrow and T. N. L. Patterson [SIAM J. Numer. Anal. 15, 953–976 (1978; Zbl 0402.65013)], Y. Xu [J. Approx. Theory 87, No. 2, 220–238 (1996; Zbl 0864.41002)], and W. Erb et al. [Numer. Math. 133, No. 4, 685–705 (2016; Zbl 1350.41008)]. We use Newton polynomials and divided differences and an apparently new formula for determinants of certain divided difference matrices.
MSC:
| 65D05 | Numerical interpolation |
| 41A05 | Interpolation in approximation theory |
| 41A10 | Approximation by polynomials |
| 41A63 | Multidimensional problems |
| 65D25 | Numerical differentiation |
| 65F40 | Numerical computation of determinants |
References:
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