A numerical differentiation method based on legendre expansion with super order Tikhonov regularization

Zhenyu Zhao and Lei You

Applied Mathematics and Computation, 2021, vol. 393, issue C

Abstract: The aim of this paper is to develop a method based on Legendre expansion to compute numerical derivatives of a function from its perturbed data. The Tikhonov regularization combined with a new penalty term is used to deal with the ill posed-ness of the problem. It has been shown that the solution process is uniform for various smoothness of functions. Moreover, the convergence rates can be obtained self-adaptively when we choose the regularization parameter by a discrepancy principle. Numerical tests show that the method gives good results.

Keywords: Numerical differentiation; Ill posed problem; Super order Tikhonov regularization; Legendre approximation; Discrepancy principle (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300320307645
Full text for ScienceDirect subscribers only

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:eee:apmaco:v:393:y:2021:i:c:s0096300320307645

DOI: 10.1016/j.amc.2020.125811

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().