Letter to the editor: Numerical differentiation for high orders by an integration method

Authors:
Zewen Wang;Rongsheng Wen
Affiliations:
School of Mathematics and Informational Science, East China Institute of Technology, Fuzhou City, Jiangxi Province, 344000, PR China;School of Mathematics and Informational Science, East China Institute of Technology, Fuzhou City, Jiangxi Province, 344000, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

This paper mainly studies the numerical differentiation by integration method proposed first by Lanczos. New schemes of the Lanczos derivatives are put forward for reconstructing numerical derivatives for high orders from noise data. The convergence rate of these proposed methods is O(@d^4^n^+^4) as the noise level @d-0. Numerical examples show that the proposed methods are stable and efficient.