| 求解Lavrentiev迭代方程的多尺度快速配置算法 |
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| 引用本文： | 杨素华,欧阳兆福,罗兴钧,彭玉兵. 求解Lavrentiev迭代方程的多尺度快速配置算法[J]. 数学年刊A辑(中文版), 2017, 38(4): 419-432 |
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| 作者姓名： | 杨素华 欧阳兆福 罗兴钧 彭玉兵 |
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| 作者单位： | 赣南师范大学数学与计算机科学学院, 江西 赣州 341000.,赣南师范大学数学与计算机科学学院, 江西 赣州 341000.,赣南师范大学数学与计算机科学学院, 江西 赣州 341000.,赣南师范大学数学与计算机科学学院, 江西 赣州 341000. |
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| 基金项目： | 本文受到国家自然科学基金(No.11361005,No.11761010,No.61502107),江西省自然科学基金(No.20151BAB201011)和江西省研究生创新基金(No.YC2015-S376)的资助. |
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| 摘 要： | 考虑了第一类Fredholm积分方程的求解.采用有矩阵压缩策略的多尺度配置方法来离散Lavrentiev迭代方程,在积分算子是弱扇形紧算子时,给出近似解的先验误差估计,并给出了改进的后验参数的选择方法,得到了近似解的收敛率.最后,举例说明算法的有效性.
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| 关 键 词： | Fredholm integral equation of the first kind Iterated Lavrentiev regularization Multiscale collocation method A posteriori parameter choice strategy |
| 收稿时间： | 2015-07-23 |
| 修稿时间： | 2016-09-26 |
Fast Multiscale Collocation Methods for Solving Iterated Lavrentiev Equations |
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| YANG Suhu,OUYANG Zhaofu,LUO Xingjun and PENG Yubing. Fast Multiscale Collocation Methods for Solving Iterated Lavrentiev Equations[J]. Chinese Annals of Mathematics, 2017, 38(4): 419-432 |
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| Authors: | YANG Suhu OUYANG Zhaofu LUO Xingjun PENG Yubing |
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| Affiliation: | School of Mathematics and Computer Science, Gannan Normal University,Ganzhou 341000, Jiangxi, China.,School of Mathematics and Computer Science, Gannan Normal University,Ganzhou 341000, Jiangxi, China.,School of Mathematics and Computer Science, Gannan Normal University,Ganzhou 341000, Jiangxi, China. and School of Mathematics and Computer Science, Gannan Normal University,Ganzhou 341000, Jiangxi, China. |
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| Abstract: | The authors consider ill-posed Fredholm integral equations of the first kind.The authors apply a multiscale collocation method with a matrix compressionstrategy to discretize the iterated Lavrentiev equation and then analyze thepriori convergence of the multiscale collocation method, if the integraloperator is the weakly sectorial operator. The convergence rates of theiterated Lavrentiev regularization are achieved by using a modified aposteriori parameter choice strategy. Finally, numerical examples are given to illustrate the efficiency of the method. |
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| Keywords: | Fredholm integral equation of the first kind Iterated Lavrentiev regularization Multiscale collocation method A posteriori parameter choice strategy |
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