| 最优投影策略下解病态积分方程的快速迭代算法 |
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| 引用本文： | 罗兴钧,李繁春,杨素华.最优投影策略下解病态积分方程的快速迭代算法[J].计算数学,2011,33(1):1-14. |
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| 作者姓名： | 罗兴钧 李繁春 杨素华 |
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| 作者单位： | 赣南师范学院数学与计算机科学学院, 江西赣州 341000 |
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| 基金项目： | 国家自然科学基金资助项目(11061001)、江西省自然科学基金资助项目(2008GZS0025)与江西省教育厅科学技术研究资助项目(GJJ10586). |
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| 摘 要： | 基于最优的投影方法,构造了求解病态积分方程的截断快速Tikhonov迭代算法,与传统投影方法相比得到了相同的最优收敛率,但内积的计算个数少于传统投影方法.同时,给出了后验参数选择办法.算例证实了算法的有效性.
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| 关 键 词： | 病态积分方程 迭代Tikhonov正则化 投影方法 后验参数选择 |
| 收稿时间： | 2009-03-02 |
A FAST ITERATIVE METHODS FOR SOLVING THE ILL-POSED INTEGRAL EQUATION BASED ON THE OPTIMAL PROJECTION METHODS |
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| Luo Xingjun,Li Fanchun,Yang Suhua.A FAST ITERATIVE METHODS FOR SOLVING THE ILL-POSED INTEGRAL EQUATION BASED ON THE OPTIMAL PROJECTION METHODS[J].Mathematica Numerica Sinica,2011,33(1):1-14. |
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| Authors: | Luo Xingjun Li Fanchun Yang Suhua |
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| Institution: | School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, Jiangxi, China |
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| Abstract: | In this paper, an adaptive discretization Tikhonov iterative method is established for solving the ill-posed integral equation based on the optimization of projection method. Compared with the usual projection technique, we obtain the best order to accuracy,but less inner products. Also,a posteriori parameter choice strategies is proposed. Finally, numerical experiments are given to illustrate the efficiency of the method. |
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| Keywords: | Ill-posed integral equations Iterated Tikhonov regularization Optimization of projection methods A posteriori parameter choice |
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