کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4607031 1631418 2015 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On weak tractability of the Smolyak algorithm for approximation problems
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
On weak tractability of the Smolyak algorithm for approximation problems
چکیده انگلیسی

We consider the problems of LpLp-approximation of dd-variate analytic functions defined on the cube with directional derivatives of all orders bounded by 1. For 1≤p<∞1≤p<∞, it is shown that the Smolyak algorithm based on polynomial interpolation at the extrema of the Chebyshev polynomials leads to weak tractability of these problems. This gives an affirmative answer to one of the open problems raised recently by Hinrichs et al. (2014). Our proof uses the polynomial exactness of the algorithm and an explicit bound on the operator norm of the algorithm.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 192, April 2015, Pages 347–361
نویسندگان
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