Scattered data interpolation based upon bivariate recursive polynomials

摘要

In this paper, firstly, based on new recursive algorithms of non-tensor-product-typed bivariate divided differences, scattered data interpolation schemes are constructed in the cases of odd and even interpolating nodes, respectively. Moreover, the corresponding error estimation is worked out, and equivalent formulae are obtained between bivariate high-order non-tensor-product-typed divided differences and high-order partial derivatives. Furthermore, the operation count for the addition/subtractions, multiplication, and divisions approximates O(n2) in the computation of the interpolating polynomials presented, while the operation count approximates O(n3) in the case of radial basis functions for sufficiently large n. Finally, several numerical examples show that it is valid for the recursive interpolating polynomial schemes, and these interpolating polynomials change as the order of the interpolating nodes, although the node collection is the same.