从矩阵的特性对线性互补算例进行分类  

Categorizing Examples of Linear Complementary Problem Based on the Characteristics of Matrices

作　　者：雍龙泉[1,2] YONG Long-quan(School of Mathematics and Computer Science Shaanxi University of Technology,Hanzhong 723001 China;Shaanxi Key Laboratory of Industrial Automation,Hanzhong 723001,China)

机构地区：[1]陕西理工大学数学与计算机科学学院,陕西汉中723001 [2]陕西省工业自动化重点实验室,陕西汉中723001

出　　处：《数学的实践与认识》2020年第24期295-303,共9页Mathematics in Practice and Theory

基　　金：陕西省教育厅重点科学科研计划项目(20JS021);陕西理工大学科研项目(SLGYQZX2002)。

摘　　要：对散落于各类文献中的线性互补算例,从矩阵角度进行分类汇总.对线性互补问题中矩阵的正定性进行了深入研究,给出了矩阵正定性的判别方法:用定义判别及用对称分量的正定性判别.进而以矩阵的对称性和正定性作为分类的依据,把线性互补算例分为5类.每一类都给出了若干算例,分析了算例中矩阵的特点,并给出了线性互补问题的解.这为研究线性互补提供了测试平台.In this paper,examples of linear complementary problem(LCP)scattered in various literatures are classified and summarized from the perspective of matrix.Positive definite of matrix in LCP is studied in depth,and the methods of whether the matrices are positive definite are presented.One is the definition,another way is research positive definite of its symmetric components.Based on the symmetry and positive definite of the matrix,the examples of linear complementary problem are divided into 5 categories.Some examples are given for each class,the characteristics of the matrix in LCP are analyzed,and the solution of the linear complementarity problem is given.This provides a test platform for studying linear complementarity problem.

关 键 词：线性互补 矩阵 对称性 正定性 测试平台 

分 类 号：O151.21[理学—数学]