Ostrowski-Brauer Sparse B (OBS-B) 矩阵及其线性互补问题的误差界  

Ostrowski-Brauer Sparse B(OBS-B)matrices and error bounds for linear complementarity problems

作　　者：刘毅 井霞 高磊 LIU Yi;JING Xia;GAO Lei(School of Mathematics and Information Science,Baoji University of Arts and Sciences,Baoji 721013,Shaanxi,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

出　　处：《云南大学学报（自然科学版）》2021年第2期205-213,共9页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(31600299);陕西省自然科学基础研究计划(2020JM-622);云南省教育厅科学研究基金(2019J0910).

摘　　要：P-矩阵在科学工程计算中发挥着重要作用.基于Ostrowski-Brauer Sparse(OBS)矩阵的定义,引入一类新的P-矩阵子类——Ostrowski-Brauer Sparse B(OBS-B)矩阵,该矩阵类包含B-矩阵和DB-矩阵.进一步,利用OBS矩阵逆的无穷大范数估计式,给出了OBS-B矩阵线性互补问题的误差界,并证明了在一定条件下所给误差界优于García-Esnaola和Peña给出的经典误差界.最后,通过数值算例对所得结果进行了说明.P-matrices play a critical role in scientific engineering calculations.Based on Ostrowski-Brauer Sparse(OBS)matrices,a new subclass of P-matrices called Ostrowski-Brauer Sparse B(OBS-B)matrices is introduced,which contains B-matrices and DB-matrices.Moreover,using the infinity norm bound of the inverse of OBS matrices,a computable error bound for the linear complementarity problem of OBS-B matrices is given.And it is shown that the given bound improves the classical bound provided for B-matrices by García-Esnaola and Peña in some cases.Finally,numerical examples are reported to illustrate the effectiveness of the obtained bound.

关 键 词：OBS-B矩阵 P-矩阵 线性互补 误差界 

分 类 号：O241[理学—计算数学]