Stable Numerical Differentiation Algorithms Based on the Fourier Transform in Frequency Domain

Yanling He, Huilin Xu and Xiaoyan Xiang
Additional contact information
Yanling He: College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China
Huilin Xu: College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China
Xiaoyan Xiang: College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China

Academic Journal of Applied Mathematical Sciences, 2022, vol. 8, issue 2, 34-41

Abstract: A class of stable numerical differential algorithms is constructed based on the Fourier transform. The instability of the numerical differentiation problem is overcome by modifying the integral “kernel†in the frequency domain. The convergence of the approximate derivatives is ensured based on some reasonable assumptions of the modified “kernel†function. The a-posteriori choice strategy of the regularization parameter is considered. Moreover, the convergence analysis and error estimate of the approximate derivatives are also given.

Keywords: Numerical differentiation; Fourier transform; ill-posedness; regularization parameter. (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.arpgweb.com/pdf-files/ajams8(2)34-41.pdf (application/pdf)
https://www.arpgweb.com/journal/17/archive/04-2022/2/8 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arp:ajoams:2022:p:34-41

DOI: 10.32861/ajams.82.34.41

Access Statistics for this article

Academic Journal of Applied Mathematical Sciences is currently edited by Dr. Diana Bílková

More articles in Academic Journal of Applied Mathematical Sciences from Academic Research Publishing Group Rahim Yar Khan 64200, Punjab, Pakistan.
Bibliographic data for series maintained by Managing Editor ().