预条件下高阶2PPJ迭代法及比较定理  

Preconditioned High order 2PPJ iterative method and comparison theorems

作　　者：黄江玲 Huang Jiangling(School of Mathematics and Statistics,Shaanxi Normal University,Xi’an710119,China)

机构地区：[1]陕西师范大学数学与统计学院,陕西西安710119

出　　处：《六盘水师范学院学报》2021年第5期100-108,共9页Journal of Liupanshui Normal University

摘　　要：当线性方程组的系数矩阵A为不含任何零元素L-阵时,给出一类新的预条件矩阵P1=I+S1,首先研究预条件P1=I+S1下的Jacobi迭代法的敛散性比较定理,其次根据Jacobi迭代矩阵与高阶2PPJ迭代矩阵之间的关系,得到了预条件P1=I+S1下的高阶2PPJ迭代法的敛散性比较定理,最后给出3个数值算例对结论加以验证。When the coefficient matrix A of the linear equation system is an L matrix without any zero elements,a new type of preconditioning matrix P1=I+S1 is given.Firstly,the convergence and divergence of the Jacobi iteration method under the preconditions is studied.Secondly,according to the relationship between the Jacobi iterative matrix and the high-order 2PPJ iterative matrix,the convergence and divergence comparison theorem of the high-order 2PPJ iterative method under the preconditions is obtained,Finally,three numerical examples are proposed to verify the conclusions.

关 键 词：L-阵 JACOBI迭代法 高阶2PPJ迭代法 预条件 比较定理 

分 类 号：O241.6[理学—计算数学]