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Reconstruction of high order derivatives by new mollification methods
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作者 赵振宇 贺国强 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第6期769-778,共10页
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 spec... 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. 展开更多
关键词 ill-posed problem numerical differentiation mollification method L generalized solution cTSVD method
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Detection of Edge with the Aid of Mollification Based on Wavelets
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作者 Tohru Morita Ken-Ichi Sato 《Applied Mathematics》 2014年第18期2849-2861,共13页
In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study h... In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study here the application of that method to the detection of edge of a function. Mathieu et al. proposed the CRONE detector for a detection of an edge of an image. For a function without noise, we note that the CRONE detector is expressed as the Riesz fractional derivative (fD) of the derivative. We study here the application of the mollification to the calculation of the Riesz fD of the derivative for a data involving noise, and compare the results with the results obtained by our method of applying simple derivative to mollified data. 展开更多
关键词 mollification EDGE DETECTOR RIESZ Fractional Derivative Mollifiers Based on WAVELETS Gibbs Phenomenon PRIMITIVE CRONE fD DETECTOR
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Determination of an Unknown Time-dependent Heat Source from A Nonlocal Measurement by Finite Difference Method 被引量:5
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作者 Ze-wen WANG Zhou-sheng RUAN +1 位作者 He-lu HUANG Shu-fang QIU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2020年第1期151-165,共15页
In this paper,we consider an inverse time-dependent source problem of heat conduction equation.Firstly,the ill-posedness and conditional stability of this inverse source problem is analyzed.Then,a finite difference in... In this paper,we consider an inverse time-dependent source problem of heat conduction equation.Firstly,the ill-posedness and conditional stability of this inverse source problem is analyzed.Then,a finite difference inversion method is proposed for reconstructing the time-dependent source from a nonlocal measurement.The existence and uniqueness of the finite difference inverse solutions are rigorously analyzed,and the convergence is proved.Combined with the mollification method,the proposed finite difference inversion method can obtain more stable reconstructions from the nonlocal data with noise.Finally,numerical examples are given to illustrate the efficiency and convergence of the proposed finite difference inversion method. 展开更多
关键词 INVERSE source PROBLEM ILL-POSED PROBLEM finite DIFFERENCE heat equation mollification
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