Filtered Legendre expansion method for numerical differentiation at the boundary point with application to blood glucose predictions
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.
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.Additional details
- Eprint ID
- 43367
- DOI
- 10.1016/j.amc.2013.09.015
- Resolver ID
- CaltechAUTHORS:20140114-144724003
- DMS-0908037
- NSF
- W911NF-09-1-0465
- Army Research Office (ARO)
- P25424
- Austrian Fonds Zur Förderung der Wissenschaftlichen Forschung (FWF)
- Created
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2014-01-14Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field