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A Stable Approach for Numerical Differentiation by Local Regularization Method with its Regularization Parameter Selection Strategies

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

Academic Journal of Applied Mathematical Sciences, 2021, vol. 7, issue 1, 27-35

Abstract: The local regularization method for solving the first-order numerical differentiation problem is considered in this paper. The a-priori and a-posteriori selection strategy of the regularization parameter is introduced, and the convergence rate of local regularization solution under some assumption of the exact derivative is also given. Numerical comparison experiments show that the local regularization method can reflect sharp variations and oscillations of the exact derivative while suppress the noise of the given data effectively.

Keywords: Local regularization; Numerical differentiation; Regularization parameter; Discrepancy principle. (search for similar items in EconPapers)
Date: 2021
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