加权差分代换与型的非负性判定  

The Weighted Difference Substitutions and Nonnegativity Decision of Forms

作　　者：侯晓荣[1] 徐松[1,2] 邵俊伟[1] 

机构地区：[1]电子科技大学自动化工程学院,成都611731 [2]宁波大学理学院,宁波315211

出　　处：《数学学报（中文版）》2010年第6期1171-1180,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家重点基础研究发展规划基金(2004CB318000);国家自然基金资助项目(10571095)

摘　　要：本文从几何的视角来研究加权差分代换,引入代换集序列收敛性概念,证明了逐次加权差分代换是收敛的.并据此给出正定型在逐次加权差分代换下可正向终止的一个严格的证明,得到了不定型在逐次加权差分代换下可负向终止并自动输出反例的一个算法.This paper provides a geometric perspective to study the weighted difference substitutions and introduces the concept of convergence of the sequence of substitution sets.Then it proves the convergence of the sequence of the successive weighted difference substitution sets,from which it is strictly proved that the sequence of the successive weighted difference substitution sets of a positive definite form is positively terminating. Finally,an algorithm for deciding an indefinite form with a counter-example is proposed.

关 键 词：加权差分代换 型的非负性判定 重心重分 

分 类 号：O187[理学—数学]