On stable numerical differentiation
TL;DR: In this article, two different approaches for numeri- cal differentiation are considered based on a regularized Volterra equation and disretized version of the regularized VOLTERRA equation.
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Abstract: Based on a regularized Volterra equation, two different approaches for numeri- cal differentiation are considered. The first approach consists of solving a regularized Volterra equation while the second approach is based on solving a disretized version of the regularized Volterra equation. Numerical experiments show that these methods are efficient and compete fa- vorably with the variational regularization method for stable calculating the derivatives of noisy functions.
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Citations
A numerical differentiation method and its application to reconstruction of discontinuity
TL;DR: In this article, a new simple method for choosing regularization parameters is proposed based on the conditional stability estimate for this ill-posed problem, and it has an almost optimal convergence rate when the exact solution is in H2.
117
On numerical differentiation algorithms for nonlinear estimation
Sette Diop,Jessy W. Grizzle,F. Chaplais +2 more
- 12 Dec 2000
TL;DR: This communication presents theoretical as well as implementation details on several numerical differentiation algorithms which may be useful in the area of nonlinear estimation.
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Numerical differentiation from a viewpoint of regularization theory
Shuai Lu,Sergei V. Pereverzev +1 more
TL;DR: New rules are proposed 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, which are shown to be effective for the differentiation of noisy functions.
82
Reconstruction of numerical derivatives from scattered noisy data
TL;DR: Based on the thin plate spline approximation theory, an effective regularization algorithm for the reconstruction of numerical derivatives from two-dimensional scattered noisy data is proposed in this paper, where the convergence results under two different choice rules for the regularization parameter are given.
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A Fictitious Time Integration Method for the Numerical Solution of the Fredholm Integral Equation and for Numerical Differentiation of Noisy Data, and Its Relation to the Filter Theory
Chein-Shan Liu,Satya N. Atluri +1 more
TL;DR: In this paper, the Fictitious Time Integration Method (FTIM) is employed to solve a system of ill-posed linear algebraic equations, which may result from the discretization of a first-kind lin- ear Fredholm integral equation.
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TL;DR: Methods of numerical integration will lead you to always think more and more, and this book will be always right for you.
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