On Further Study of Bivariate Polynomial Interpolation over Ortho-Triples

On Further Study of Bivariate Polynomial Interpolation over Ortho-Triples

Year:    2018

Numerical Mathematics: Theory, Methods and Applications, Vol. 11 (2018), Iss. 2 : pp. 247–271

Abstract

In this paper, based on the recursive algorithm of the non-tensor-product-typed bivariate divided differences, the bivariate polynomial interpolation is reviewed firstly. And several numerical examples show that the bivariate polynomials change as the order of the ortho-triples, although the interpolating node collection is invariant. Moreover, the error estimation of the bivariate interpolation is derived in several cases of special distributions of the interpolating nodes. Meanwhile, the high order bivariate divided differences are represented as the values of high order partial derivatives. Furthermore, the operation count approximates $\mathcal{O}(n^2)$ in the computation of the interpolating polynomials presented, including the operations of addition/substraction, multiplication, and division, while the operation count approximates $\mathcal{O}(n^3)$ based on radial basis functions for sufficiently large $n$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2017-0042

Numerical Mathematics: Theory, Methods and Applications, Vol. 11 (2018), Iss. 2 : pp. 247–271

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords: