Volume 11, Issue 2
On Further Study of Bivariate Polynomial Interpolation over Ortho-Triples

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 247-271.

Published online: 2018-11

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• 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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@Article{NMTMA-11-247, author = {}, title = {On Further Study of Bivariate Polynomial Interpolation over Ortho-Triples}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {2}, pages = {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 $n$.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0042}, url = {http://global-sci.org/intro/article_detail/nmtma/12429.html} }
TY - JOUR T1 - On Further Study of Bivariate Polynomial Interpolation over Ortho-Triples JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 247 EP - 271 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.OA-2017-0042 UR - https://global-sci.org/intro/article_detail/nmtma/12429.html KW - AB -

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 $n$.

Jiang Qian, Fan Wang, Yisheng Lai & Qingjie Guo. (2020). On Further Study of Bivariate Polynomial Interpolation over Ortho-Triples. Numerical Mathematics: Theory, Methods and Applications. 11 (2). 247-271. doi:10.4208/nmtma.OA-2017-0042
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