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Error analysis for a class of numerical differentiator

Da-Yan Liu 1, 2 Dayan Liu Olivier Gibaru 2, 3 Wilfrid Perruquetti 2, 4
2 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Centrale Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
4 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : This report is devoted to derivatives estimations. Contrary to the Tikhonov's regularization procedure, we use a recent algebraic framework which involves finally a projection into the Jacobi polynomial basis so as to estimate these derivatives from noisy data. No information about the statistical properties of the noise is required. We give some results concerning the choice of the parameters of this method so as to minimize the noise error contribution and the approximation errors. Moreover, two new central estimators based on such algebraic differentiation techniques are introduced. A comparison is done between these estimations and some of the improved classical numerical differentiation schemes.
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Submitted on : Friday, February 5, 2021 - 10:15:20 PM
Last modification on : Thursday, January 20, 2022 - 4:16:36 PM


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  • HAL Id : inria-00439386, version 2



Da-Yan Liu, Dayan Liu, Olivier Gibaru, Wilfrid Perruquetti. Error analysis for a class of numerical differentiator. [Intern report] Inria Lille - Nord Europe. 2009. ⟨inria-00439386v2⟩



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