Almost optimal differentiation using noisy data
type: Item
instance of: scholarly article
title: Almost optimal differentiation using noisy data
zbMATH Open document ID: 0860.65010
author: Klaus Ritter
published in: Journal of Approximation Theory
publication date: 1996-10-27T00:00:00Z
review text: Differentiation of functions \(f\) is studied if only inaccurate data \(f(t_i)+\varepsilon_i\) are available, the \(f\) being stochastic and corrupted by some noise \(\varepsilon_i\), the function \(f\) being observed at a finite number of points. Expressions are derived for the derivative \(f^{(k)}\) either at a single point \(t\in [0,1]\) or on the whole interval \([0,1]\). In this latter case the distance from \(f^{(k)}\) in \(L_2\)-norm is considered. Optimality of smoothing spline methods is discussed. An expression is also found for the order of minimal errors for recovering \(f^{(k)}\) in the interval \([0,1]\).
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 65D10
zbMATH DE Number: 938744
zbMATH Keywords: noisy data
zbMATH Keywords: numerical differentiation
zbMATH Keywords: smoothing spline methods
MaRDI profile type: Publication
full work available at URL: jath.1996.0071
OpenAlex ID: W2084424440
DOI: 10.1006/JATH.1996.0071
description: scientific article; zbMATH DE number 938744