Journal Article10.1137/0708026
Numerical Differentiation and Regularization
TL;DR: In this paper, Tikhonov's regularization procedure is applied to the operation of differentiation, resulting in a procedure for numerical differentiation for which the effects of errors in the values of the function being differentiated on the values for the derivative obtained in the procedure can be studied.
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Abstract: Tikhonov’s regularization procedure is applied to the operation of differentiation, resulting in a procedure for numerical differentiation for which the effects of errors in the values of the function being differentiated on the values for the derivative obtained in the procedure can be studied. The theoretical discussion is complemented by the results of numerical experiments.
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Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy
TL;DR: It is shown that the weighted cross-validation estimate of $\hat \lambda $ estimates the value of $\lambda $ which minimizes $({1 / n) E\sum
olimits_{j = 1}^n {[(\mathcal{K}f_{n,\lambda } )(t_j ) - (\mathcal(K)f)(t-j )]} ^2 $ .
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Numerical Differentiation of Noisy, Nonsmooth Data
TL;DR: This work uses total-variation regularization, which allows for discontinuous solutions in the differentiation process, and accurately differentiates noisy functions, including those which have a discontinuous derivative.
Technique for the evaluation of derivatives from noisy biomechanical displacement data using a model-based bandwidth-selection procedure.
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TL;DR: In this article, an autoregressive model is fitted to the signal, and low-pass filtering is performed in the frequency domain by a linear phase FIR filter and differentiation is performed on the high-frequency noise magnification.
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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.
A comparison of automatic filtering techniques applied to biomechanical walking data
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References
•Book
Theory of Ordinary Differential Equations
Earl A. Coddington,Norman Levinson +1 more
- 01 Jan 1955
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.
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