拟-Nekrasov型矩阵逆的无穷范数上界及其应用  

An upper bound of the infinity norm for the inverse of quasi-Nekrasov-type matrices and its application

作　　者：李娟 贾秀丹 周平 赵天绪 LI Juan;JIA Xiu-dan;ZHOU Ping;ZHAO Tian-xu(School of Mathematics and Information Science,Baoji University of Arts and Sciences,Baoji 721013,Shaanxi,China;School of Mathematics and Engineering,Wenshan University,Wenshan 663099,Yunnan,China)

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013 [2]文山学院数学与工程学院,云南文山663099

出　　处：《宝鸡文理学院学报（自然科学版）》2023年第2期23-28,34,共7页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：陕西省创新人才推进计划项目(2022KJXX-01);云南省教育厅科学研究基金项目(2022J0949);宝鸡文理学院研究生科研创新重点项目(YJSCX22ZD04)

摘　　要：目的提出一类新的非奇异矩阵:拟-Nekrasov型矩阵,研究其逆矩阵无穷范数的上界及在线性互补问题中的应用。方法利用QN-矩阵的定义、矩阵分解与不等式放缩技术进行研究。结果与结论给出了拟-Nekrasov型矩阵的定义,证明了其为非奇异H-矩阵的子类,推广了严格对角占优矩阵类,数值例子表明拟-Nekrasov型矩阵类与QN-矩阵类互不包含;给出了拟-Nekrasov型矩阵逆矩阵无穷范数的一个上界,证明了其优于经典的Varah界,同时得到了拟-Nekrasov型矩阵线性互补问题的误差界,数值算例阐明了所给误差界的优越性。PurposesTo propose a new class of nonsingular matrices:Quasi-Nekrasov-type matrices,and give and apply an upper bound of the infinity norm for quasi-Nekrasov-type matrices to the linear complementarity problems.MethodsThe research is conducted according to the definition of the quasi-Nekrasov-type matrices,matrix factorization,and inequality scaling techniques.Results and ConclusionsThe concept of the quasi-Nekrasov-type matrices is given,which generalizes the strictly diagonally dominant matrices,and proved to be a subclass of nonsingular H-matrices.Numerical examples show that neither quasi-Nekrasov-type matrices and QN-matrices are included in each other.Meanwhile,an upper bound of the infinity norm for the inverse of quasi-Nekrasov-type matrices is given,which improves the classical Varah's bound.Based on the proposed bound,an error bound for the linear complementarity problem of quasi-Nekrasov-type matrices is obtained,and the numerical examples are given to illustrate the effectiveness of the proposed error bound.

关 键 词：拟-Nekrasov型矩阵 H-矩阵 无穷范数 线性互补问题 误差界 

分 类 号：O241[理学—计算数学]