| 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Pα1→k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. |
| 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 |
| DOI： |
| 分类号:O241.6 |
| 基金项目:Supported by National Natural Science Foundation of China (61273311; 61303223). |
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| COMPARISON THEOREMS FOR A CLASS OFPRECONDITIONED AOR ITERATIVE METHODS |
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XUE Qiu-fang1,2, GAO Xing-bao1, LIU Xiao-guang1
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1.College of Math. and Infor. Science, Shaanxi Normal University, Xi'an 710062, China;2.Department of Applied Math., Xi'an University of Technology, Xi'an 710048, China
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| Abstract: |
| In this paper, the preconditioned AOR iterative methods with the preconditioners Pα1→k are 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 parameters α 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. |
| Key words: preconditioner preconditioned AOR iterative method strictly diagonally dominant L-matrix spectral radius |
