摘要
主要分析了差分代换矩阵的基本性质，证明了存在有限个差分代换矩阵的乘积可以将单位点（1，0，…，0）变换到指定的非负（本原）整点．利用这一结果可以导出R^n＋上判定半正定型的充要条件．根据此充要条件建立的算法（TSDS）可能不停机，针对不停机的情况，再给出一些判定半正定型的充分条件．
Some essential properties of so-called difference substitution matrices are given, and it is proven that there are a finitely many difference substitution matrices whose product transforms the unit point （1, 0,..., 0） into a specified integral point with nonnegative components. A sufficient and necessary condition for the nonnegativity of a polynomial on R^n＋ w is obtained by using this result. Since the procedure based on the above arguments sometimes may not terminate, some sufficient conditions for the nonnegativity of polynomials in nonterminating cases are proposed.
出处
《系统科学与数学》
CSCD
北大核心
2009年第9期1169-1177,共9页
Journal of Systems Science and Mathematical Sciences
基金
国家重点基础研究发展规划项目(2004CB318003)
国家自然科学基金重点项目(90718041)
中国科学院知识创新工程重要方向(KJCX-YW-S02)资助项目
关键词
差分代换矩阵
差分代换集序列
终止性
半正定型
Difference substitution matrices, set sequence of difference substitution,termination, positive semidefinite form.
