摘要
本文研究块Toeplitz方程组的块Gauss-Seidel迭代算法.我们首先讨论了块三角Toeplitz矩阵的一些性质,然后给出了求解块三角Toeplitz矩阵逆的快速算法,由此而得到了求解块Toeplitz方程组的快速块Gauss-Seidel迭代算法,最后证明了当系数矩阵为对称正定和H-矩阵时该方法都收敛.数值例子验证了方法的收敛性.
The block Gauss - Seidel iterations for solving block Toeplitz systems are considered in this paper. We first discuss some properties of block triangular Toeplitz matrices, then present fast algorithms for finding the inverses of such matrices, and further obtain fast block Gauss - Seidel iterative algorithms for block Toeplitz systems. Finally, we show that our methods are convergent when the coefficient matrices are symmetric positive definite or H - matrices. Some numerical examples demonstrate the convergence of our schemes.
出处
《数学理论与应用》
2012年第1期1-5,共5页
Mathematical Theory and Applications
基金
湖南省教育厅重点资助项目(09A002[2009])
