α-块对角占优矩阵与两类迭代法的收敛性  

α-block Diagonally Dominant Matrices and the Convergence of Two Kinds of Iterative Methods

作　　者：傅河清 蔡静[1] 高寿兰[1] FU Heqing;CAI Jing;GAO Shoulan(School of Science,Huzhou University,Huzhou 313000,China)

机构地区：[1]湖州师范学院理学院,浙江湖州313000

出　　处：《湖州师范学院学报》2022年第8期1-5,共5页Journal of Huzhou University

基　　金：教育部高校特色专业建设点(教高函〔2008121〕号);国家自然科学基金项目(11871249).

摘　　要：探讨两类α-块对角占优矩阵,利用矩阵非奇异性和迭代矩阵的谱半径估计,证明当系数矩阵为这两类块对角占优矩阵时,线性方程组Ax=b的块Jacobi迭代法和块Guass Seidel迭代法均收敛.In this paper,two classes ofαdiagonally dominant block matrices are discussed.By using the nonsingularity of the matrix and the estimation of the spectral radius of the iterative matrix,it is proved that when the coefficient matrix belongs to these two classes,the block Jacobi iterative method and the block Guass Seidel iterative method for system of linear equations are convergent.

关 键 词：块对角占优矩阵 JACOBI迭代法 Guass Seidel迭代法 非奇异性 谱半径 

分 类 号：O241.6[理学—计算数学]