二元再生核与最佳 Hermite 插值逼近算子

Bivariate Reproducing Kernel and the Best Hermite Interpolation Operators

应用再生核理论，给出了一类二元函数的非多项式型的最佳Ｈｅｒｍｉｔｅ插值逼近算子的具体表达式，并证明了它对散乱节点系的一致收敛性及误差在范数意义下的单调下降性．

By theory of reproducing kernel,the explicit representation of the best Hermite interpolation operators for a class of bivariate functions is given,which is not in the polynomial form;meanwhile,it is proved to be convergent uniformly to the system of scramble nodes,and the error of interpolation decreases monotonically in space norm