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Indexed by:期刊论文

Date of Publication:2018-05-01

Journal:NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS

Included Journals:SCIE

Volume:11

Issue:2

Page Number:247-271

ISSN No.:1004-8979

Key Words:Bivariate polynomial interpolation; non-tensor product type; error estimation; ortho-triple; radial basis function

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 O(n(2)) in the computation of the interpolating polynomials presented, including the operations of addition/substractions, multiplication, and divisions, while the operation count approximates O(n(3)) based on radial basis functions for sufficiently large n.