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论文类型：期刊论文

发表时间：2018-05-01

发表刊物：NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS

收录刊物：SCIE

卷号：11

期号：2

页面范围：247-271

ISSN号：1004-8979

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

摘要：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.