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Filtered Legendre expansion method for numerical differentiation at the boundary point with application to blood glucose predictions

Mhaskar, Hrushikesh N. and Naumova, V. and Pereverzyev, S. V. (2013) Filtered Legendre expansion method for numerical differentiation at the boundary point with application to blood glucose predictions. Applied Mathematics and Computation, 224 . pp. 835-847. ISSN 0096-3003. doi:10.1016/j.amc.2013.09.015. https://resolver.caltech.edu/CaltechAUTHORS:20140114-144724003

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Abstract

Let ƒ:[-1,1]→R be continuously differentiable. We consider the question of approximating ƒ′(1) from given data of the form tj,ƒ(tj)^M_(j-1) where the points t_j are in the interval [-1,1]. It is well known that the question is ill-posed, and there is very little literature on the subject known to us. We consider a summability operator using Legendre expansions, together with high order quadrature formulas based on the points t_j’s to achieve the approximation. We also estimate the effect of noise on our approximation. The error estimates, both with or without noise, improve upon those in the existing literature, and appear to be unimprovable. The results are applied to the problem of short term prediction of blood glucose concentration, yielding better results than other comparable methods.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.amc.2013.09.015DOIArticle
http://www.sciencedirect.com/science/article/pii/S0096300313009879PublisherArticle
Additional Information:© 2013 Elsevier Inc. Published: Nov 1 2013. The research of the first author was supported, in part, by grant DMS-0908037 from the National Science Foundation and grant W911NF-09-1-0465 from the US Army Research Office. The second and third authors are supported by the Austrian Fonds Zur Förderung der Wissenschaftlichen Forschung (FWF), Grant P25424.
Funders:
Funding AgencyGrant Number
NSFDMS-0908037
Army Research Office (ARO)W911NF-09-1-0465
Austrian Fonds Zur Förderung der Wissenschaftlichen Forschung (FWF)P25424
Subject Keywords: Numerical differentiation; Legendre polynomials; Blood glucose prediction
DOI:10.1016/j.amc.2013.09.015
Record Number:CaltechAUTHORS:20140114-144724003
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140114-144724003
Official Citation:Hrushikesh N. Mhaskar, V. Naumova, S.V. Pereverzyev, Filtered Legendre expansion method for numerical differentiation at the boundary point with application to blood glucose predictions, Applied Mathematics and Computation, Volume 224, 1 November 2013, Pages 835-847, ISSN 0096-3003, http://dx.doi.org/10.1016/j.amc.2013.09.015. (http://www.sciencedirect.com/science/article/pii/S0096300313009879)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:43367
Collection:CaltechAUTHORS
Deposited By:INVALID USER
Deposited On:14 Jan 2014 23:18
Last Modified:10 Nov 2021 16:36

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