M-矩阵线性互补问题和扩展垂直线性互补问题解的新误差界  

NEW ERROR BOUNDS FOR LINEAR COMPLEMENTARITY PROBLEMS OF M-MATRICES AND EXTENDED VERTICAL LINEAR COMPLEMENTARITY PROBLEM OF INTERVAL M-MATRICES

作　　者：王何慧 李朝迁[2] Wang Hehui;Li Chaoqian(Jingmen Vocational College,Jingmen 448000;School of Mathematics and Statistics,Yunnan University,Kunming 650091)

机构地区：[1]荆门职业学院,荆门448000 [2]云南大学数学与统计学院,昆明650091

出　　处：《高等学校计算数学学报》2024年第1期55-64,共10页Numerical Mathematics A Journal of Chinese Universities

摘　　要：1引言给定矩阵M∈R^(n×n)和向量q∈R^(n),求向量x∈Rn使之满足{Mx+q≥0,x≥0,x^(T)(Mx+q)=0,或者证明不存在这样的向量x,称上述问题为线性互补问题,记为LCP(M,q).线性互补问题在最优化理论[1],神经网络模型[2],控制论[3]等方面有着广泛的运用,一直是优化、计算数学等领域的热门研究问题[4-7].A new error bound of the M-matrix linear complementarity problem is obtained by the properties of interval M-matrices.We also obtain error bounds of the extended vertical linear complementarity problem of interval M-matrices.Numerical examples are given to illustrate the validity of the obtained results.

关 键 词：线性互补问题 计算数学 最优化理论 误差界 控制论 神经网络模型 热门研究 

分 类 号：O151.21[理学—数学]