| 求解第一类Fredholm积分方程的一种新的正则化算法 |
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| 引用本文： | 李功胜,刘岩. 求解第一类Fredholm积分方程的一种新的正则化算法[J]. 数学研究及应用, 2005, 25(2): 204-210 |
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| 作者姓名： | 李功胜 刘岩 |
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| 作者单位： | 1. 山东理工大学数学学院应用数学所,山东,淄博,255049
2. 黄河水利职业技术学院基础部,河南,开封,475001 |
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| 基金项目： | Natural Science Foundation of Shandong Province (Y2001E03) |
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| 摘 要： | 应用一种新的正则化方法建立了一类新的求解第一类Fredholm积分方程的正则化算法, 并借助Matlab软件给出了数值算例.数值结果与理论分析基本一致,而且表明文中建立的正则化比通常的Tikhonov正则化更精确.
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| 关 键 词： | 第一类Fredholm积分方程 病态问题 改进的Tikhonov正则化算法 正则解的渐近阶 数值分析 |
| 收稿时间： | 2002-10-28 |
A New Regularizing Algorithm for Solving the First Kind of Fredholm Integral Equations |
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| LI Gong-sheng and LIU Yan. A New Regularizing Algorithm for Solving the First Kind of Fredholm Integral Equations[J]. Journal of Mathematical Research with Applications, 2005, 25(2): 204-210 |
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| Authors: | LI Gong-sheng and LIU Yan |
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| Affiliation: | Inst. of Appl. Math.; Shandong University of Technology; Zibo; China;Yellow River Conservancy Technical Institute; Kaifeng; China |
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| Abstract: | Singular value system is applied to construct a new class of improved regularizing methods for solving the first kind of Fredholm integral equations with noisy data. By a priori choosing regularizing parameters, optimal convergence order of the regularized solution is obtained. And with aids of MATLAB software, numerical results are presented which roughly coincide with the theoretical analysis. |
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| Keywords: | first kind of Predholm integral equation ill-posed problem modified Tikhonov regularization asymptotic order of the regularized solution numerical analysis. |
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