Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems.
Electron. J. Diff. Eqns., Conference 21 (2014), pp. 235-246.

Methods for numerical differentiation of noisy data

Ian Knowles, Robert J. Renka

We describe several methods for the numerical approximation of a first derivative of a smooth real-valued univariate function for which only discrete noise-contaminated data values are given. The methods allow for both uniformly distributed and non-uniformly distributed abscissae. They are compared for accuracy on artificial data sets constructed by adding Gaussian noise to simple test functions. We also display results associated with an experimental data set.

Published February 10, 2014.
Math Subject Classifications: 65D10, 65D25, 65R32.
Key Words: Ill-posed problem; numerical differentiation; smoothing spline; Tikhonov regularization; total variation.

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Ian Knowles
Department of Mathematics
University of Alabama at Birmingham
Birmingham AL 35294, USA
Robert J. Renka
Department of Computer Science & Engineering
University of North Texas
Denton, TX 76203-1366, USA

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