| L-曲线估计确定正则参数的双网格迭代法 |
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| 引用本文： | 吴国丽 李维国. L-曲线估计确定正则参数的双网格迭代法[J]. 数学理论与应用, 2006, 26(4): 8-12 |
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| 作者姓名： | 吴国丽 李维国 |
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| 作者单位： | 中国石油大学数学与计算科学学院，中国石油大学数学与计算科学学院 东营，257061，东营，257061 |
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| 摘 要： | 本文考虑对不适定问题离散化得到的大规模不适定线性方程组进行Tiknonov正则化,然后用双网格迭代法求解得到的Tikhonov正则化方程组,并用L-曲线估计法来确定正则参数.试验问题的数值结果表明双网格迭代法求解正则化后的对称正定线性方程组效果很好,且L-曲线估计法确定正则参数计算量很小.
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| 关 键 词： | 不适定问题 正则化 L-曲 共轭梯度法 预优因子 迭代法 |
| 收稿时间： | 2006-04-05 |
| 修稿时间： | 2006-04-05 |
L-Curve Curvature Bounds in Two--Grid Iterative Methods |
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| Wu Guoli ,Li Weiguo. L-Curve Curvature Bounds in Two--Grid Iterative Methods[J]. Mathematical Theory and Applications, 2006, 26(4): 8-12 |
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| Authors: | Wu Guoli Li Weiguo |
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| Affiliation: | School of Mathematics and Computational Science,University of Petroleum,Dong Ying,257061 |
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| Abstract: | Large scaled ill-conditionedlinear systems arising from discretization of ill-posed problems are considered and Tikhonov regularization is used.The two-grid methods are introduced to solve the regularized systems.The estimation of L-curve is applied to determine a suitable value of the regularization parameter.The numerical results of some test problems show that the two-grid methods are robust in solving regularized systems.The work of the computation of the estimation of the L-curve is little. |
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| Keywords: | ill-posed problem regularization L-curve conjugate gradient preconditioners iterative methods |
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