| 求解半正定病态积分方程的多尺度快速Lavrentiev迭代算法 |
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| 引用本文： | 罗兴钧,谢长发娣,陈维君,李繁春.求解半正定病态积分方程的多尺度快速Lavrentiev迭代算法[J].赣南师范学院学报,2012(6):1-5. |
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| 作者姓名： | 罗兴钧 谢长发娣 陈维君 李繁春 |
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| 作者单位： | 赣南师范学院数学与计算机科学学院 |
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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(20114BAB201014);江西省教育厅科学技术研究资助项目(GJJ10586) |
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| 摘 要： | 基于多尺度投影方法,构造了求解半正定病态积分方程的截断快速Lavrentiev迭代算法,并给出了新的后验参数选择办法.与传统全投影方法相比,减少了内积计算个数,保持了最优收敛率.最后,算例验证了算法的有效性.
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| 关 键 词： | 病态积分方程 迭代Lavrentiev正则化 截断投影方法 后验参数选择办法 |
A Fast Lavrentiev Iterative Methods for Solving the Semi-definite Ill-posed Integral Equation Based on the Truncated Projection Method |
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| LUO Xingjun,XIECHANG Fadi,CHEN Weijun,LI Fanchun.A Fast Lavrentiev Iterative Methods for Solving the Semi-definite Ill-posed Integral Equation Based on the Truncated Projection Method[J].Journal of Gannan Teachers' College(Social Science(2)),2012(6):1-5. |
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| Authors: | LUO Xingjun XIECHANG Fadi CHEN Weijun LI Fanchun |
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| Institution: | (School of Mathematics and Computer Science,Gannan Normal University,Ganzhou 3 41000,China) |
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| Abstract: | In this paper,a fast iterative Lavrentiev method is established for so lving the semi-definite ill-posed integral equation based on the optimization of projection method,and a posteriori parameter choice strategy of improvement is proposed.Compared with the traditional projection technique,we keep the optima l convergence rate,but less than the number of inner products caculation.Finall y,numerical experiments are given to illustrate the efficiency of the method. |
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| Keywords: | ill-posed integral equations iterated lavrentiev regularization trun cated projection methods a posteriori parameter choice strategy |
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