多元三角阵列插值的基表示

The Basis Expression of Multivariate Triangular Matrix Interpolation

本文提出一种多元多项式插值,概括了目前已有的几类插值.文中给出了插值公式的构造方法,得出插值分式的显式表现,进而分析了该插值公式的误差估计.

A generalization of univariate triangular matrix (definite or indefinite) has been drawn in multivariate Euclid spaces R^s in this paper (by Micchelli's divided differences). Some previous interpolation methods, such as Newton interpolation, Kergin Interpolation, Abel-Goncharov interpolation, Hakopian interpolation and multivariate quasi-Newton interpolation, are the especial examples of our method. We prove the existence and uniqueness of the interpolation problem, and the explicit formulas of the interpolatory polynomials are established by so-called interpolatory basis functions which have the recursive properties (also partly, see[1]). Our main result is Theorem 4 which asserts that the partial derivatives of the interpolatory remainder can be written as linear combination of lower order Micchelii's divided differences. As corolary of Theorem 4, we give the estimation of the remainder in norm.