Reconstruction of high order derivatives by new mollification methods

• Published in: Applied mathematics and mechanics Vol. 29; no. 6; pp. 769 - 778
• Main Author: 赵振宇 贺国强
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University Press 01.06.2008; College of Sciences, Guangdong Ocean University, Zhanjiang 524088, Guangdong Province, P. R. China%College of Sciences, Shanghai University, Shanghai 200444, P. R. China; College of Sciences, Shanghai University, Shanghai 200444, P. R. China
• Subjects: Algorithms; Applications of Mathematics; Classical Mechanics; Derivatives; Fluid- and Aerodynamics; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Partial Differential Equations; Reconstruction; Regularization; 数值分化; 数值分析; 求解方法; 软化作用; numerical differentiation; O241; cTSVD method; 65D25; 47A52; ill-posed problem; mollification method; generalized solution; L generalized solution
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-008-0608-y

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.