截断策略下求解第一类积分方程离散的DSM方法

doi:10.12286/jssx.2012.2.139

计算数学 ›› 2012, Vol. 34 ›› Issue (2): 139-152.DOI: 10.12286/jssx.2012.2.139

截断策略下求解第一类积分方程离散的DSM方法

罗兴钧¹, 陈维君¹, 范林秀¹, 李繁春²

1. 赣南师范学院数学与计算机科学学院, 江西赣州 341000;
2. 江西应用技术职业学院基础教学部, 江西赣州 341000

收稿日期:2011-04-19 出版日期:2012-05-15 发布日期:2012-05-20
基金资助:
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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罗兴钧, 陈维君, 范林秀, 李繁春. 截断策略下求解第一类积分方程离散的DSM方法[J]. 计算数学, 2012, 34(2): 139-152.

Luo Xingjun, Chen Weijun, Fan Linxiu, Li Fanchun. THE DISCRETIZATION OF THE DSM METHODS FOR SOLVING THE ILL-POSED INTEGRAL EQUATION OF THE FIRST KIND BASED ON THE TRUNCATED STRATEGY[J]. Mathematica Numerica Sinica, 2012, 34(2): 139-152.

THE DISCRETIZATION OF THE DSM METHODS FOR SOLVING THE ILL-POSED INTEGRAL EQUATION OF THE FIRST KIND BASED ON THE TRUNCATED STRATEGY

Luo Xingjun¹, Chen Weijun¹, Fan Linxiu¹, Li Fanchun²

1. School of Mathematics and computer science, GanNan Normal University, Ganzhou 341000, Jiangxi, China;
2. Department of Basic Teaching Ministry, Jiangxi Vocational College of Applied Technology, Ganzhou 341000, Jiangxi, China

Received:2011-04-19 Online:2012-05-15 Published:2012-05-20

本文用多尺度投影方法求解离散的DSM问题,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, 算例说明了算法的有效性.

关键词： 病态积分方程, Tikhonov 正则化, 动力系统方法, 多尺度投影, 后验参数选择

In this paper, we develop a fast multiscale projection method to solve the discretization of the DSM problem. Compared with the traditional projection technique, we keep the optimal convergence rate, but less than the number of inner products calculation. Finally, numerical experiments are given to illustrate the efficiency of the method.

Key words: Ill-posed integral equations, Tikhonov regularization, multiscale projection method, Dynamical systems methods, A posteriori parameter choice strategy.

MR(2010)主题分类:

65J20
65J10

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摘要

截断策略下求解第一类积分方程离散的DSM方法

THE DISCRETIZATION OF THE DSM METHODS FOR SOLVING THE ILL-POSED INTEGRAL EQUATION OF THE FIRST KIND BASED ON THE TRUNCATED STRATEGY

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