重构高阶导数的磨光方法

doi:10.1007/s10483-008-0608-y

Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (6): 769-778 .doi: https://doi.org/10.1007/s10483-008-0608-y

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

收稿日期:2007-07-24 修回日期:2008-03-20 出版日期:2008-06-18 发布日期:2008-06-18
通讯作者: 贺国强

Reconstruction of high order derivatives by new mollification methods

ZHAO Zhen-yu^1,2, HE Guo-qiang¹

1. College of Sciences,~~Shanghai University, Shanghai 200444, P. R. China;
2. College of Sciences,~~Guangdong Ocean University,Zhanjiang 524088,Guangdong Province, P. R. China

Received:2007-07-24 Revised:2008-03-20 Online:2008-06-18 Published:2008-06-18
Contact: HE Guo-qiang

摘要/Abstract

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（典型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。

关键词: 不适定问题, L-广义解, 磨光方法, 数值微分, 典型TSVD方法

Abstract: In this paper, the problem of reconstructing numerical derivatives from noisy data is considered. A new framework of mollification methods based on the L
generalized solution regularization methods is proposed. A specific algorithm for the first three derivatives is presented in the paper, in which a modification of TSVD, termed cTSVD is chosen as the regularization technique. Numerical examples given in the paper verify the theoretical results and show efficiency of the new method.

Key words: mollification method, L generalized solution, cTSVD method, ill-posed problem, numerical differentiation

中图分类号:

赵振宇;贺国强. 重构高阶导数的磨光方法[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(6): 769-778 .

ZHAO Zhen-yu;HE Guo-qiang. Reconstruction of high order derivatives by new mollification methods[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(6): 769-778 .

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重构高阶导数的磨光方法

Reconstruction of high order derivatives by new mollification methods

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