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Tower节点集上的极小次数牛顿基

陈 涛, 董 天, 张树功   

  1. 吉林大学 数学学院, 长春 130012
  • 收稿日期:2007-10-08 修回日期:1900-01-01 出版日期:2007-11-26 发布日期:2007-11-26
  • 通讯作者: 张树功

Minimal Degree Newton Basis for Interpolation on Tower Sets

CHEN Tao, DONG Tian, ZHANG Shugong   

  1. College of Mathematics, Jilin University, Changchun 130012, China
  • Received:2007-10-08 Revised:1900-01-01 Online:2007-11-26 Published:2007-11-26
  • Contact: ZHANG Shugong

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Grobner基的快速算法.

关键词: tower节点集, 多元多项式插值, 极小次数牛顿基

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.

Key words: tower set, multivariate polynomial interpolation, minimal degree Newton basis

中图分类号: 

  • O241.3