| 块Toeplitz方程组的快速块Gauss-Seidel迭代算法 |
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| 引用本文： | 冯月华,刘成志,刘仲云.块Toeplitz方程组的快速块Gauss-Seidel迭代算法[J].数学理论与应用,2012(1):1-5. |
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| 作者姓名： | 冯月华 刘成志 刘仲云 |
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| 作者单位： | 长沙理工大学数学与计算科学学院 |
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| 基金项目： | 湖南省教育厅重点资助项目(09A002[2009]) |
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| 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。
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| 关 键 词： | 块Toeplitz 块Gauss-Seidel迭代 快速算法对称正定H-阵 |
Fast Block Gauss-Seidel Iterations for Toeplitz Systems |
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| Feng Yuehua Liu Chengzhi Liu Zhongyun.Fast Block Gauss-Seidel Iterations for Toeplitz Systems[J].Mathematical Theory and Applications,2012(1):1-5. |
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| Authors: | Feng Yuehua Liu Chengzhi Liu Zhongyun |
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| Institution: | Feng Yuehua Liu Chengzhi Liu Zhongyun(School of Mathematics and Computing Science,Changsha University of Science and Technology, Changsha,410004,P.R.China) |
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| Abstract: | 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. |
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| Keywords: | Block Toeplitz Block Gauss-Seidel iteration Fast algorithm Symmetric positive definite H-matrices |
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