کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9501288 1338399 2005 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Information-based nonlinear approximation: an average case setting
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Information-based nonlinear approximation: an average case setting
چکیده انگلیسی
Nonlinear approximation (NA) has usually been studied under deterministic assumptions and complete information about the underlying functions. In the present paper we assume only partial information, e.g., function values at some points, and we are interested in the average case error and complexity of NA. We show that the problem can be essentially decomposed in two independent problems related to average case nonlinear (restricted) approximation from complete information, and to average case unrestricted approximation from partial information. The results are then applied to average case piecewise polynomial approximation on C([0,1]) based on function values with respect to r-fold Wiener measure. In this case, to approximate with error ɛ it is necessary and sufficient to know the function values at Θɛ-1ln1/2(1/ɛ)1/(r+1/2) equidistant points and use Θɛ-1/(r+1/2) adaptively chosen break points in piecewise polynomial approximation.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 21, Issue 2, April 2005, Pages 211-229
نویسندگان
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