α-双对角占优与非奇异H-矩阵的判定  

α-double diagonal dominance and the criterions for nonsingular H-matrices

作　　者：李阳[1] 宋岱才[1] 路永洁[1] 

机构地区：[1]辽宁石油化工大学理学院,辽宁抚顺113001

出　　处：《合肥工业大学学报（自然科学版）》2005年第12期1624-1626,共3页Journal of Hefei University of Technology：Natural Science

基　　金：辽宁省科学技术基金资助项目(001084)

摘　　要：设A=(aij∈Cn×n),若α∈[0,1],使对i≠j(i,j∈〈n〉),均有aijaj j≥(RiRj)α(SiSj)1-α,则称A为α-双对角占优矩阵;一方面,利用矩阵的有向图的方法指出了不可约和α-双对角占优矩阵为非奇异H-矩阵的一个充分条件;另一方面研究了一类具不可约和α-双对角占优矩阵为H-矩阵的必要条件,进一步丰富和完善了α-双对角占优与非奇异H-矩阵的理论。Let A=（αij∈Cn×n）, if there exists E α∈ [-0,1] which can make ｜αiiαij｜≥（RiRj）^n（SiSj）^1-n be right for ↓A i≠j（i,j∈（n））, then A is called an α-doubly diagonally dominant matrix. By the method of matrix＇s directed graphs,a sufficient condition for an irreducible and α-doubly diagonally dominant matrix to be a nonsingular H-matrix is presented,and a necessary condition for a kind of irreducible and α-doubly diagonally dominant matrix to be a nonsingular H-matrix is studied. This study enriches and improves the theory of α-doubly diagonally dominant and nonsingular H-matrices.

关 键 词：不可约矩阵 双对角占优 H-矩阵 

分 类 号：O151.21[理学—数学]