Title
Adaptive parameter choice for one-sided finite difference schemes and its application in diabetes technology
Abstract
In this paper we discuss the problem of approximation of the first derivative of a function at the endpoint of its definition interval. This problem is motivated by diabetes therapy management, where it is important to provide estimations of the future blood glucose trend from current and past measurements. A natural way to approach the problem is to use one-sided finite difference schemes for numerical differentiation, but, following this way, one should be aware that the values of the function to be differentiated are noisy and available only at given fixed points. Then (as we argue in the paper) the number of used point values is the only parameter to be employed for regularization of the above mentioned ill-posed problem of numerical differentiation. In this paper we present and theoretically justify an adaptive procedure for choosing such a parameter. We also demonstrate some illustrative tests, as well as the results of numerical experiments with simulated clinical data.
Year
DOI
Venue
2012
10.1016/j.jco.2012.06.001
J. Complexity
Keywords
DocType
Volume
illustrative test,future blood glucose trend,adaptive procedure,diabetes technology,numerical experiment,adaptive parameter choice,one-sided finite difference scheme,definition interval,past measurement,ill-posed problem,diabetes therapy management,numerical differentiation
Journal
28
Issue
ISSN
Citations 
5-6
0885-064X
2
PageRank 
References 
Authors
0.41
5
3
Name
Order
Citations
PageRank
V Naumova1305.06
Sergei Pereverzev2978.07
S. Sivananthan3182.10