کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4643360 | 1341377 | 2006 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Pointwise convergence of Fourier regularization for smoothing data
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
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چکیده انگلیسی
The classical smoothing data problem is analyzed in a Sobolev space under the assumption of white noise. A Fourier series method based on regularization endowed with generalized cross validation is considered to approximate the unknown function. This approximation is globally optimal, i.e., the mean integrated squared error reaches the optimal rate in the minimax sense. In this paper the pointwise convergence property is studied. Specifically, it is proved that the smoothed solution is locally convergent but not locally optimal. Examples of functions for which the approximation is subefficient are given. It is shown that optimality and superefficiency are possible when restricting to more regular subspaces of the Sobolev space.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 196, Issue 2, 15 November 2006, Pages 540-552
Journal: Journal of Computational and Applied Mathematics - Volume 196, Issue 2, 15 November 2006, Pages 540-552
نویسندگان
Daniela De Canditiis, Italia De Feis,