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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Numerical differentiation by integration
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by Xiaowei Huang, Chuansheng Wu and Jun Zhou PDF
Math. Comp. 83 (2014), 789-807 Request permission

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.
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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
  • 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).
  • © Copyright 2013 American Mathematical Society
  • Journal: Math. Comp. 83 (2014), 789-807
  • MSC (2010): Primary 65J20; Secondary 65D25
  • DOI: https://doi.org/10.1090/S0025-5718-2013-02722-6
  • MathSciNet review: 3143692