کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4640172 1341264 2011 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Differentiation by integration with Jacobi polynomials
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Differentiation by integration with Jacobi polynomials
چکیده انگلیسی

In this paper, the numerical differentiation by integration method based on Jacobi polynomials originally introduced by Mboup et al. [19] and [20] is revisited in the central case where the used integration window is centered. Such a method based on Jacobi polynomials was introduced through an algebraic approach [19] and [20] and extends the numerical differentiation by integration method introduced by Lanczos (1956) [21]. The method proposed here, rooted in [19] and [20], is used to estimate the nnth (n∈Nn∈N) order derivative from noisy data of a smooth function belonging to at least Cn+1+q(q∈N)Cn+1+q(q∈N). In [19] and [20], where the causal and anti-causal cases were investigated, the mismodelling due to the truncation of the Taylor expansion was investigated and improved allowing a small time-delay in the derivative estimation. Here, for the central case, we show that the bias error is O(hq+2)O(hq+2) where hh is the integration window length for f∈Cn+q+2f∈Cn+q+2 in the noise free case and the corresponding convergence rate is O(δq+1n+1+q) where δδ is the noise level for a well-chosen integration window length. Numerical examples show that this proposed method is stable and effective.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 235, Issue 9, 1 March 2011, Pages 3015–3032
نویسندگان
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