Knowles, Ian; Renka, Robert J. Methods for numerical differentiation of noisy data. (English) Zbl 1287.65016 Electron. J. Differ. Equ. 2014, Conf. 21, 235-246 (2014). Summary: 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. Cited in 16 Documents MSC: 65D25 Numerical differentiation 65D07 Numerical computation using splines 65D10 Numerical smoothing, curve fitting Keywords:ill-posed problem; numerical differentiation; smoothing spline; Tikhonov regularization; total variation Software:TSPACK PDFBibTeX XMLCite \textit{I. Knowles} and \textit{R. J. Renka}, Electron. J. Differ. Equ. 2014, 235--246 (2014; Zbl 1287.65016) Full Text: EMIS