一类预条件AOR迭代法的比较定理(英文)  

COMPARISON THEOREMS FOR A CLASS OF PRECONDITIONED AOR ITERATIVE METHODS

作　　者：薛秋芳[1,2] 高兴宝[1] 刘晓光[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062 [2]西安理工大学应用数学系,陕西西安710048

出　　处：《数学杂志》2014年第3期448-460,共13页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(61273311;61303223)

摘　　要：本文研究了当线性方程组的系数矩阵是严格对角占优L-矩阵时带有预条件子P1→kα的预条件AOR迭代方法.利用矩阵分裂的相关理论,获得了预条件AOR迭代法的收敛性结论以及参数α和k对收敛速度影响的比较定理.结果表明当α和k取值较大时这类预条件方法更加有效.文中的结论推广了Li等人关于预条件Gauss-Seidel迭代法的相关结论.最后,用数值例子进一步验证了这些结果.In this paper, the preconditioned AOR iterative methods with the preconditioners P1→kαare studied when the coefficient matrix of the linear system is a strictly diagonally dominant L-matrix. By using the related theories of matrix splitting, the convergence performance of the preconditioned AOR methods and the comparison theorems about the influence of the parametersα and k on the rate of convergence are obtained. The results indicate that the preconditioners with the big k and α are efficient and competitive for the preconditioned AOR methods. The results in the paper generalize those about the preconditioned Gauss-Seidel methods given by Li et al.Numerical examples further verify the results.

关 键 词：预条件子 预条件AOR迭代法 严格对角占优L-矩阵 谱半径 

分 类 号：O241.6[理学—计算数学]