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 - <p style="text-align: justify;">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 $n$.</p>