Tower节点集上的极小次数牛顿基

将关于张量积格点的lower子集上Lagrange插值问题的极小次数牛顿基推广到tower节点子集上. 解决了二元Lagrange插值牛顿基问题, 把tower节点集的概念推广到任意多维情形， 以三维为例给出了相应的Lagrange插值极小次数牛顿基,并给出了计算三维tower节点集合消逝理想的约化Grobner基的快速算法.

Minimal Degree Newton Basis for Interpolation on Tower Sets

The minimal degree Newton basis for Lagrange interpolation on a lower subset of a tensor product grid that is proposed by Gasca and Sauer was extended to a tower subset of the grid. At first, we solved the bivariate cases. Furthermore, we extended the notion of a 2-dimensional tower set to arbitrary high dimensions and then gave the minimal degree Newton basis for trivariate Lagrange interpolation on a tower set as an example. Finally, we introduced a fast algorithm for constructing the reduced Grobner basis for the vanishing ideal of a 3-dimensional tower set.