重构高阶导数的磨光方法

赵振宇; 贺国强

重构高阶导数的磨光方法

赵振宇^1,2,
贺国强¹

1.
上海大学理学院,上海 200444;2.广东海洋大学理学院,广东湛江 524088

详细信息

作者简介:
赵振宇(1977- ),男,河北唐山人,博士(E-mail:wozitianshanglai@163.com);贺国强(1946- ),男,浙江镇海人,教授(联系人.Tel:+86-21-66134464;E-mail:gqhe@staff.shu.edu.cn).

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出版历程
- 收稿日期: 2007-09-24
- 修回日期: 2008-03-24
- 刊出日期: 2008-06-15

Reconstruction of High Order Derivatives by New Mollification Methods

ZHAO Zhen-yu^1,2,
HE Guo-qiang¹

1.
College of Science, Shanghai University, Shanghai 200444, P. R. China;

摘要

摘要: 考虑由扰动数据重构原函数的导数问题．基于L-广义解正则化理论，提出了一个新的磨光方法的框架．给出一个具体的求解前3阶导数的算法,其中正则化策略选择了一种改进的TSVD(truncated singular value decomposition)方法(典则TSVD方法)．数值结果进一步验证了理论结果及新方法的有效性．
- 不适定问题 /
- 数值微分 /
- 磨光方法 /
- L-广义解 /
- 典则TSVD方法
Abstract: The problem of reconstructing numerical derivatives from noisy data is considered. A new framework of mollification methods based on L-generalized solution regularization methods was proposed. A concrete algorithm for the first three derivatives was presented, in which a modification of TSVD (called cTSVD (canonical truncated singular value decomposition)) is chosen as the needed regularization technique. The numerical examples given verify the theoretical results and show the efficiency of the new method.
- illposed problem /
- numerical differentiation /
- mollification method /
- L-generalized solution /
- cTSVD method

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参考文献(16)

[1]	Gorenflo R,Vessella S.Abel Integral Equations,Analysis and Application,Lecture Notes in Mathematics[M].Berlin:Springer-verlag,1991.
[2]	Deans S R.Radon Transform and Its Applications[M].New York:A Wiley-Interscience Publication,John Wiley & Sons Inc,1983.
[3]	Hanke M,Scherzer O.Inverse problems light:numerical differentiation[J].Amer Math Monthly,2001,108(6):512-521. doi: 10.2307/2695705
[4]	Murio D A.The Mollification Method and the Numerical Solution of Ill-Posed Problems[M].New York:A Wiley-Interscience Publication,John Wiley & Sons Inc,1993.
[5]	Murio D A, Mejia C E,Zhan S.Discrete mollification and automatic numerical differentiation[J].Compute Math Appl,1998,35(5):1-16.
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[7]	Khan I R,Ohba R.New finite difference formulas for numerical differentiation[J].J Compu Appl Math,2000,126(1/2):269-276. doi: 10.1016/S0377-0427(99)00358-1
[8]	Wang Y B,Hon Y C,Cheng J.Reconstruction of high order derivatives from input data[J].J Inverse Ill-Posed Probl,2006,14(1):205-218. doi: 10.1515/156939406777571085
[9]	Wei T,Li M.High order numerical derivatives for one-dimensional scattered noisy data[J]. Appl Math Comput,2006,175(2):1744-1759. doi: 10.1016/j.amc.2005.09.018
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[14]	He G Q.A TSVD form for ill-posed equations leading to optimal convergence rates[A].In:ICM 2002,Abstracts of Short Communication and Poster Sessions[C].Beijing:Higher Edu Press,2002,328.
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重构高阶导数的磨光方法

作者简介:
赵振宇(1977- ),男,河北唐山人,博士(E-mail:wozitianshanglai@163.com);贺国强(1946- ),男,浙江镇海人,教授(联系人.Tel:+86-21-66134464;E-mail:gqhe@staff.shu.edu.cn).

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Reconstruction of High Order Derivatives by New Mollification Methods

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重构高阶导数的磨光方法

作者简介: 赵振宇(1977- ),男,河北唐山人,博士(E-mail:wozitianshanglai@163.com);贺国强(1946- ),男,浙江镇海人,教授(联系人.Tel:+86-21-66134464;E-mail:gqhe@staff.shu.edu.cn).

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出版历程

Reconstruction of High Order Derivatives by New Mollification Methods

计量

出版历程

目录

作者简介:
赵振宇(1977- ),男,河北唐山人,博士(E-mail:wozitianshanglai@163.com);贺国强(1946- ),男,浙江镇海人,教授(联系人.Tel:+86-21-66134464;E-mail:gqhe@staff.shu.edu.cn).