P矩阵的新子类:DBπ^R矩阵和MBπ^R矩阵  

New subclasses of P-matrices:DBπ^R-matrices and MBπ^R-matrices

作　　者：呼慧 刘毅 高磊 HU Hui;LIU Yi;GAO Lei(School of Science, Inner Mongolia University of Technology, Hohhot 010051, Inner Mongolia, China;School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China)

机构地区：[1]内蒙古工业大学理学院,内蒙古呼和浩特010051 [2]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《宝鸡文理学院学报（自然科学版）》2020年第4期1-5,共5页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：陕西省自然科学基础研究计划项目(2020JM-622);云南省教育厅科技计划项目(2019J0910);宝鸡文理学院校级重点项目(ZK2017021)。

摘　　要：目的P矩阵在科学工程计算中发挥着重要作用,然而如何判定P矩阵比较困难,因此给出简单易行的P矩阵判定条件。方法根据Bπ^R矩阵和DB矩阵的定义,并结合矩阵分裂的方法进行研究。结果提出2类新矩阵:DBπ^R矩阵和MBπ^R矩阵,并证明了它们均为P矩阵;进一步研究了DBπ^R矩阵和MBπ^R矩阵的相关性质及与其他P矩阵子类之间的关系。给出P矩阵新的判定条件,提出非奇异矩阵类:DBπ^R矩阵,并给出其等价条件。结论所得结果可应用于实矩阵特征值的估计以及线性互补问题误差分析中。Purposes—To give simple and easy criteria for verifying P-matrix because it is difficult to check whether a given matrix is a P-matrix or not in general although P-matrices play a critical role in the calculations of scientific engineering.Methods—Motivated by the definitions of Bπ^R-matrices and DB-matrices,and combined with the matrix splitting technique,some new criteria for verifying P-matrix are constructed.Result—Two new subclasses of P-matrices are introduced which are called DBπ^R-matrices and MBπ^R-matrices,and it is proved that they are both P-matrices.Further,the properties and the relations between Bπ^R-matrices and DBRπ-matrices are discussed.Some new criteria for verifying P-matrix are provided,with a new class of nonsingular matrices named DBπ^R-matrices given and its equivalent conditions presented.Conclusion—These results can be applied to the localization of the real parts of all eigenvalues of a real matrix and the error analysis of the linear complementarity problem.

关 键 词：P矩阵 Bπ^R矩阵 DBπ^R矩阵 MBπ^R矩阵 

分 类 号：O241[理学—计算数学]