Splitting iterations for circulant‐plus‐diagonal systems
Splitting iterations for circulant‐plus‐diagonal systems
复制标题
DOI：
10.1002/nla.451
复制
发表时间：
2005-10
影响因子：
4.3
通讯作者：
Man-Kiu Ho;M. Ng
中科院分区：
文献类型：
--
作者：
Man-Kiu Ho;M. Ng
考虑线性方程组（C + iD）x=B，其中C是循环矩阵，D是真实的对角矩阵.我们研究了构造这种系数矩阵的正常/斜厄米特分裂的技术。理论结果表明，当C的特征值具有正的真实的部分时，分裂法收敛于线性方程组的精确解。当C的特征值具有非负真实的部分时，给出了收敛条件.我们提出了一个连续的超松弛加速计划建议分裂迭代。数值例子说明了该方法的有效性。版权所有© 2005年约翰威利父子有限公司。
We consider the system of linear equations (C + iD)x=b, where C is a circulant matrix and D is a real diagonal matrix. We study the technique for constructing the normal/skew‐Hermitian splitting for such coefficient matrices. Theoretical results show that if the eigenvalues of C have positive real part, the splitting method converges to the exact solution of the system of linear equations. When the eigenvalues of C have non‐negative real part, the convergence conditions are also given. We present a successive overrelaxation acceleration scheme for the proposed splitting iteration. Numerical examples are given to illustrate the effectiveness of the method. Copyright © 2005 John Wiley & Sons, Ltd.