一类多元全次数 Hermite 插值问题研究

A Class of Multivariate Hermite Interpolation of Total Degree

中文关键词:  多元Hermite插值  正则性  全次数

英文关键词:multivariate Hermite interpolation  regularity  total degree

中文摘要:

      本文研究了多元全次数Hermite插值问题的正则性,对于任意的维数$d$,首先证明了两组组合恒等式,然后给出两组正则的插值格式,并给出了适定结点组的一种选取方式.

英文摘要:

      In this paper we study a class of multivariate Hermite interpolation problem on $2^d$ nodes with dimension $d\geq 2$ which can be seen as a generalization of two classical Hermite interpolation problems of $d=2$. Two combinatorial identities are firstly given and then the regularity of the proposed interpolation problem is proved.