广义严格对角占优矩阵的一种判别法  

An Iterative Method for Checking Generalized Strictly Diagonally Dominant Matrices

作　　者：关晋瑞[1] 任孚鲛[1] GUAN Jinrui;REN Fujiao(Department of Mathematics, Taiyuan Normal University, Jinzhong 030619, China)

机构地区：[1]太原师范学院数学系

出　　处：《应用数学》2019年第3期676-681,共6页Mathematica Applicata

基　　金：国家自然科学基金(11401424);山西省自然科学基金(201601D011004);太原师范学院大学生创新创业训练项目(CXCY1861)

摘　　要：广义严格对角占优矩阵是一类很重要的特殊矩阵,在理论与实际中具有广泛的应用,有关它的判别一直是人们研究的重点.本文给出广义严格对角占优矩阵的一种迭代判别法,证明了相应的收敛性理论,并用数值算例展示了该判别法的有效性.Generalized strictly diagonally dominant matrix is a kind of special matrix which has many applications in theory and practice, and research on its discrimination has become a hot topic in recent years. In this paper, an iterative method is proposed for identifying a matrix to be a generalized strictly diagonally dominant matrix or not. Theoretical analysis and numerical examples are given to show that the method is effective and efficient.

关 键 词：广义严格对角占优矩阵 不可约矩阵 迭代判别法 

分 类 号：O241.6[理学—计算数学]