کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4628514 1631830 2013 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Filtered Legendre expansion method for numerical differentiation at the boundary point with application to blood glucose predictions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Filtered Legendre expansion method for numerical differentiation at the boundary point with application to blood glucose predictions
چکیده انگلیسی

Let f:[-1,1]→Rf:[-1,1]→R be continuously differentiable. We consider the question of approximating f′(1)f′(1) from given data of the form (tj,f(tj))j=1M where the points tjtj are in the interval [-1,1][-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 tjtj’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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 224, 1 November 2013, Pages 835–847
نویسندگان
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