定常二级迭代法与其外迭代法收敛性的比较

计算机工程与应用 ›› 2014, Vol. 50 ›› Issue (8): 11-15.

定常二级迭代法与其外迭代法收敛性的比较

薛秋芳1，2，高兴宝1，刘晓光1

1.陕西师范大学数学与信息科学学院，西安 710062
2.西安理工大学理学院应用数学系，西安 710054

出版日期:2014-04-15 发布日期:2014-05-30

Comparison results about stationary two-stage iterative methods and outer iterative methods

XUE Qiufang1，2, GAO Xingbao1, LIU Xiaoguang1

1.College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
2.Department of Applied Mathematics, College of Science, Xi’an University of Technology, Xi’an 710054, China

Online:2014-04-15 Published:2014-05-30

摘要/Abstract

摘要： 研究了定常二级迭代法的收敛性，得到了定常二级迭代法与其外迭代收敛率的比较定理。结果表明外迭代的收敛速度一般快于定常二级迭代法，还给出了H-矩阵迭代法的比较结论。最后，数值例子验证了结论。

关键词: 定常二级迭代法, 外迭代法, 不可约矩阵, H-矩阵, 谱半径

Abstract: In this paper, the convergence rate of stationary two-stage iterative methods is studied. Comparison results about the convergence rate of stationary two-stage iterative methods and their outer iterative methods are obtained. It is shown that the outer iterative methods are faster than the stationary two-stage iterative methods with the mild splittings. For the splittings of H-matrices, comparison results are also gotten. Finally, the obtained results are illustrated by the example.

Key words: stationary two-stage iterative method, outer iterative method, irreducible matrix, H-matrix, spectral radius

薛秋芳1，2，高兴宝1，刘晓光1. 定常二级迭代法与其外迭代法收敛性的比较[J]. 计算机工程与应用, 2014, 50(8): 11-15.

XUE Qiufang1，2, GAO Xingbao1, LIU Xiaoguang1. Comparison results about stationary two-stage iterative methods and outer iterative methods[J]. Computer Engineering and Applications, 2014, 50(8): 11-15.

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