Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Numerical differentiation from a viewpoint of regularization theory

Authors: Shuai Lu and Sergei V. Pereverzev
Journal: Math. Comp. 75 (2006), 1853-1870
MSC (2000): Primary 65D25; Secondary 65J20
Posted: May 15, 2006
MathSciNet review: 2240638
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we discuss the classical ill-posed problem of numerical differentiation, assuming that the smoothness of the function to be differentiated is unknown. Using recent results on adaptive regularization of general ill-posed problems, we propose new rules for the choice of the stepsize in the finite-difference methods, and for the regularization parameter choice in numerical differentiation regularized by the iterated Tikhonov method. These methods are shown to be effective for the differentiation of noisy functions, and the order-optimal convergence results for them are proved.

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