【摘要】 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Grbner基的快速算法.更多还原

【Abstract】 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 Grbner basis for the vanishing ideal of a 3-dimensional tower set.更多还原