| 新预条件Gauss-Seidel迭代法及收敛性比较 |
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| 引用本文： | 薄利艳,杨晋.新预条件Gauss-Seidel迭代法及收敛性比较[J].中北大学学报,2012(1):63-65,69. |
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| 作者姓名： | 薄利艳 杨晋 |
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| 作者单位： | 太原理工大学数学学院 |
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| 摘 要： | 针对Gauss-Seidel迭代法求解线性方程组,引入了一种新的预条件矩阵.当系数矩阵为广泛应用的M-矩阵时,给出了该预条件Gauss-Seidel迭代法与经典Gauss-Seidel迭代法的比较定理,其说明了新预条件Gauss-Seidel迭代法是收敛的且加速了经典Gauss-Seidel迭代法的收敛速率.证明了新预条件Gauss-Seidel迭代法优于已有预条件Gauss-Seidel迭代法.最后用一个数值例子来验证所得结论的有效性.
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| 关 键 词： | 预条件 M-矩阵 Gauss-Seidel迭代法 比较定理 |
A New Preconditioned Gauss-Seidel Iterative Method and Its Convergence |
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| BO Li-yan,YANG Jin.A New Preconditioned Gauss-Seidel Iterative Method and Its Convergence[J].Journal of North University of China,2012(1):63-65,69. |
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| Authors: | BO Li-yan YANG Jin |
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| Affiliation: | (College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China) |
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| Abstract: | A new preconditioned matrix was introduced for solving linear systems with Gauss-Seidel iterative method.Under the condition that the coefficient matrix being an M-matrix,which is widely used,the comparison theorem between preconditioned Gauss-Seidel iterative method and classic Gauss-Seidel iterative method was given.The preconditioned Gauss-Seidel iterative method is convergent and it accelerates the convergent speed of classic Gauss-Seidel iterative method.It showed that newly proposed preconditioned Gauss-Seidel iterative method is superior to the Gauss-Seidel iterative method mentioned.A numerical example was given to verify the effectiveness of the conclusions. |
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| Keywords: | precondition M-matrix Gauss-Seidel method comparison theorem |
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