Ian Knowles, Robert J. Renka
Abstract:
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 email: iknowles@uab.edu | |
Robert J. Renka Department of Computer Science & Engineering University of North Texas Denton, TX 76203-1366, USA email: robert.renka@unt.edu |
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