[1]胡彬,夏赟,喻建华.算子非精确条件下确定正则化参数的一种方法[J].江西师范大学学报(自然科学版),2014,(01):65-69.
 HU Bin,XIA Yun,YU Jian-hua.The Method for Determining Regularization Parameters with Perturbed Operators[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(01):65-69.
点击复制

算子非精确条件下确定正则化参数的一种方法()
分享到:

《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2014年01期
页码:
65-69
栏目:
出版日期:
2014-02-28

文章信息/Info

Title:
The Method for Determining Regularization Parameters with Perturbed Operators
作者:
胡彬;夏赟;喻建华
东华理工大学理学院,江西南昌,330013
Author(s):
HU Bin;XIA Yun;YU Jian-hua
关键词:
不适定问题正则化方法正则化参数模型函数广义偏差原则
Keywords:
ill-posed problemregularization methodregularization parametermodel functiongeneralized discrepancy principle
分类号:
O241.8;O241.6
文献标志码:
A
摘要:
基于非标准的广义偏差原则,在算子及观测数据都有扰动的条件下,对于求解不适定问题的Tik-honov正则化方法,给出了一种选取正则化参数的简单迭代算法,并阐明了该迭代算法是一种线性模型函数算法.进一步地,利用线性模型函数方法,在一定条件下证明了所提出的选取正则化参数的简单迭代算法是收敛的,并通过数值算例验证了该方法的有效性.
Abstract:
Based on the non-standard generalized discrepancy principle,a simple iteration method is given for choosing regularization parameters with perturbed operator and noise data for the Tikhonov regularization method,which is a classical method for solving ill-posed problems.And it is clarified that the proposed iteration method is a linear model function algorithm.Furthermore,the simple iteration method for choosing regularization parameters is proved to be converging under some conditions by using the linear model function method.Numerical experiments show that the method is efficient.

参考文献/References:

[1] Kirsch A.An Introduction to the Mathematical Theory of Problems [M].New York:Springer-Verlag,1996.
[2] Engl H W,Hanke M,Neubamer A.Regularization of problems [M].Dordrecht:Kluwer,1996.
[3] 刘继军.不适定问题的正则化方法及应用 [M].北京:科学出版社,2005.
[4] Cheng J,Yamamoto M.One new strategy for a priori choice of regularizing parameters in Tikhonovs regularization [J].Inverse Problems,200,16(4):L31-38.
[5] Kunisch K,Zou J.Iterative choices of regularization parameters in linear inverse problems [J].Inverse problems,1998,14(5):1247-1264.
[6] Xie J L.Zou J.An improved model function method for choosing regularization parameters in linear inverse problems [J].Inverse Problems,2002,18(5):631-643.
[7] Lin J J.Ni M.A model function method for determining the regularization parameter in potential approach for the recovery of scattered wave [J].Applied Numerical Mathematics,2008,58(8):113-1128.
[8] Wang Z W.Liu J J.New model function methods for determining regularization parameters in linear inverse problems [J].Applied Numerical Mathematics,2009,59(10):2489-2506.
[9] Wang Z W.Multi-parameter Tiknonov regularization and model function approach to the damped Morozov principle for choosing regularization parameters [J].Journal of Computational and Applied Mathematics.2012.236(7):1815-1832.
[10] Wang Z W,Xu D H.On the linear model function method for choosing Tikhonov regularization parameters in linear ill-posed problems,Chinese Journal of Engineering Mathematics,accepted.
[11] Tikhonov A N.Goncharsky A V.Stepanov V V.Yagola A G.Numerical methods for the solution of ill-posed problems [M].Dordrecht:Kluwer Academic,1995.
[12] 樊树芳,马青华,王彦飞.算子及观测数据都非精确情况下一种新的正则化参数选择方法 [J].北京师范大学学报:自然科学版,2006,42(1):25-31.
[13] 王彦飞.反问题的计算方法及应用 [M].北京:高等教育出版社,2007.

相似文献/References:

[1]胡彬,徐会林,王泽文,等.基于模型函数与L-曲线的正则化参数选取方法[J].江西师范大学学报(自然科学版),2014,(06):569.
 HU Bin,XU Hui-lin,WANG Ze-wen,et al.The Method for Choosing Regularization Parameters Based on a Model Function and the L-Curve[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(01):569.
[2]邱淑芳,王泽文,曾祥龙,等.一类时间分数阶扩散方程中的源项反演解法[J].江西师范大学学报(自然科学版),2018,(06):610.[doi:10.16357/j.cnki.issn1000-5862.2018.06.11]
 QIU Shufang,WANG Zewen,ZENG Xianglong,et al.The Numerical Method for Reconstructing Source Term in a Time Fractional Diffusion Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2018,(01):610.[doi:10.16357/j.cnki.issn1000-5862.2018.06.11]
[3]任丽婷,熊向团*.带有非齐次Dirichlet条件的Helmholtz方程柯西问题的傅里叶方法[J].江西师范大学学报(自然科学版),2019,(02):184.[doi:10.16357/j.cnki.issn1000-5862.2019.02.12]
 REN Liting,XIONG Xiangtuan*.The Fourier Method for the Cauchy Problem of the Helmholtz Equation with Inhomogeneous Dirichlet Data[J].Journal of Jiangxi Normal University:Natural Science Edition,2019,(01):184.[doi:10.16357/j.cnki.issn1000-5862.2019.02.12]
[4]石娟娟,熊向团*.时间反向热传导问题的拟逆正则化方法及误差估计[J].江西师范大学学报(自然科学版),2021,(01):22.[doi:10.16357/j.cnki.issn1000-5862.2021.01.03]
 SHI Juanjuan,XIONG Xiangtuan*.The Quasi-Reversibility Regularization Method and Error Estimate for the Time-Inverse Heat Conduction Problem[J].Journal of Jiangxi Normal University:Natural Science Edition,2021,(01):22.[doi:10.16357/j.cnki.issn1000-5862.2021.01.03]

备注/Memo

备注/Memo:
国家自然科学基金(11161002);江西省青年科学基金(20132BAB211014);江西省教育厅科技课题(GJJ13460)
更新日期/Last Update: 1900-01-01