Adaptive parameter choice for one-sided finite difference schemes and its application in diabetes technology
type: Item
instance of: scholarly article
title: Adaptive parameter choice for one-sided finite difference schemes and its application in diabetes technology
zbMATH Open document ID: 1253.65032
author: S. Sivananthan
author: Valeriya Naumova
author: Sergei V. Pereverzyev
published in: Journal of Complexity
publication date: 2012-10-10T00:00:00Z
review text: Let \(y\in C^r[b,\,B]\) \((r\geq 2)\). Assume that only noisy values \(y_{\delta}(t_j)\) with \(|y(t_j) - y_{\delta}(t_j)|\leq \delta\) on a grid \(b\leq t_1 < \ldots < t_{N-1}<t_N =B\) are given. Using one-sided finite difference formulas (with \(n+1\) values \(y_{\delta}(t_j)\)), the authors compute an approximate value of \(y'(B)\). The number \(n\) is used as regularization parameter of this ill-posed problem of numerical differentiation. The selection of an optimal parameter \(n\) is based on the balancing principle of \textit{S. Lu} and \textit{S. V. Pereverzev} [Math. Comput. 75, No. 256, 1853--1870 (2006; Zbl 1115.65021)]. For theoretical data as well as for simulated clinical data of diabetes therapy (of blood glucose prediction), numerical tests are shown.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 92C50
zbMATH DE Number: 6092441
zbMATH Keywords: numerical differentiation
zbMATH Keywords: one-sided finite difference formula
zbMATH Keywords: regularization parameter
zbMATH Keywords: optimal parameter
zbMATH Keywords: balancing principle
zbMATH Keywords: diabetes therapy
zbMATH Keywords: blood glucose prediction
zbMATH Keywords: numerical examples
zbMATH Keywords: ill-posed problems
MaRDI profile type: Publication
full work available at URL: j.jco.2012.06.001
OpenAlex ID: W2158933491
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DOI: 10.1016/J.JCO.2012.06.001
description: scientific article; zbMATH DE number 6092441