کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4608727 1631472 2012 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Adaptive parameter choice for one-sided finite difference schemes and its application in diabetes technology
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Adaptive parameter choice for one-sided finite difference schemes and its application in diabetes technology
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 28, Issues 5–6, October–December 2012, Pages 524–538
نویسندگان
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