Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

Request Permissions   Purchase Content 
 

 

Numerical differentiation by integration


Authors: Xiaowei Huang, Chuansheng Wu and Jun Zhou
Journal: Math. Comp. 83 (2014), 789-807
MSC (2010): Primary 65J20; Secondary 65D25
DOI: https://doi.org/10.1090/S0025-5718-2013-02722-6
Published electronically: June 4, 2013
MathSciNet review: 3143692
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Based on the Lanczos methods revived by Groetsch, a method of differentiation by integration is presented to approximate derivatives of approximately specified functions. The method is applicable for any point in a finite closed interval. Convergence estimates in $ C[a,b]$ and $ L^{p}[a,b]$ are given. Numerical examples show that the method is simple and applicable.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65J20, 65D25

Retrieve articles in all journals with MSC (2010): 65J20, 65D25


Additional Information

Xiaowei Huang
Affiliation: School of Sciences, Wuhan University of Technology, Wuhan 430070, China
Email: huangxw@whut.edu.cn

Chuansheng Wu
Affiliation: School of Sciences, Wuhan University of Technology, Wuhan 430070, China
Email: Lzywcs@whut.edu.cn

Jun Zhou
Affiliation: School of Sciences, Wuhan University of Technology, Wuhan 430070, China
Email: whjcc@163.com

DOI: https://doi.org/10.1090/S0025-5718-2013-02722-6
Keywords: Ill-posed problems, numerical differentiation, regularization parameter
Received by editor(s): February 6, 2010
Received by editor(s) in revised form: September 25, 2011, and May 24, 2012
Published electronically: June 4, 2013
Additional Notes: The first author was supported in part by the Natural Science Foundation of Hubei Province (No. 2011CDB244) and the Fundamental Research Funds for the Central Universities (No. 2011-Ia-006).
The third author was supported in part by the Fundamental Research Funds for the Central Universities (No. 2012-Ia-049).
Article copyright: © Copyright 2013 American Mathematical Society