Reconstruction of High Order Derivatives by New Mollification Methods

ZHAO Zhen-yu; HE Guo-qiang

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ZHAO Zhen-yu, HE Guo-qiang. Reconstruction of High Order Derivatives by New Mollification Methods[J]. Applied Mathematics and Mechanics, 2008, 29(6): 696-704.

Citation:

ZHAO Zhen-yu, HE Guo-qiang. Reconstruction of High Order Derivatives by New Mollification Methods[J]. Applied Mathematics and Mechanics, 2008, 29(6): 696-704.

Citation:

ZHAO Zhen-yu, HE Guo-qiang. Reconstruction of High Order Derivatives by New Mollification Methods[J]. Applied Mathematics and Mechanics, 2008, 29(6): 696-704.

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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;

Received Date: 2007-09-24
Rev Recd Date: 2008-03-24
Publish Date: 2008-06-15

Abstract

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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References(16)

References

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