| 一种新的求解第一类Fredholm积分方程正则化的数值分析 |
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| 引用本文： | 李功胜,于杰. 一种新的求解第一类Fredholm积分方程正则化的数值分析[J]. 山东理工大学学报：自然科学版, 2003, 17(2): 5-8 |
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| 作者姓名： | 李功胜 于杰 |
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| 作者单位： | 山东理工大学数学与信息科学学院，山东淄博255049 |
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| 基金项目： | 山东省自然科学基金资助项目 (Y2 0 0 1E0 3 ) |
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| 摘 要： | 应用改进的Tikhonov正则化，借助Matlab软件对一类Fredholm积分方程进行数值求解．结果表明，李功胜等所建立的改进的Tikhonov正则化比通常的Tikhonov正则化更精确，而且正则解能够达到与理论分析基本一致的较高的收敛率．
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| 关 键 词： | 第一类Fredholm积分方程 Tikhonov正则化算法 数值求解 正则解 数值分析 |
| 文章编号： | 1007-1857(2003)02-0005-04 |
| 修稿时间： | 2002-11-12 |
An Optimal Regularization Strategy for Solving the First Kind of Fredholm Integral Equations Numerical Analysis |
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| LI Gong sheng,YU Jie. An Optimal Regularization Strategy for Solving the First Kind of Fredholm Integral Equations Numerical Analysis[J]. Journal of Shandong University of Technology:Science and Technology, 2003, 17(2): 5-8 |
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| Authors: | LI Gong sheng YU Jie |
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| Abstract: | With aids of Matlab software, the modified Tikhonov regularization algorithm established by LI Gong sheng et al is applied to solve the first kind of Fredholm integral equations. The numerical results show that this new regularization scheme is more accurate than ordinary Tikhonov regularization and the regularized solution can achieve higher convergence rate, which roughly coincides with the theoretical analysis. |
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| Keywords: | the first kind of Fredholm integral equation modified Tikhonov regularization algorithm numerical analysis |
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