کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4607226 1631437 2013 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Approximation by multivariate Bernstein–Durrmeyer operators and learning rates of least-squares regularized regression with multivariate polynomial kernels
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Approximation by multivariate Bernstein–Durrmeyer operators and learning rates of least-squares regularized regression with multivariate polynomial kernels
چکیده انگلیسی

In this paper, we establish error bounds for approximation by multivariate Bernstein–Durrmeyer operators in LρXp (1≤p<∞1≤p<∞) with respect to a general Borel probability measure ρXρX on a simplex X⊂RnX⊂Rn. By the error bounds, we provide convergence rates of type O(m−γ)O(m−γ) with some γ>0γ>0 for the least-squares regularized regression algorithm associated with a multivariate polynomial kernel (where mm is the sample size). The learning rates depend on the space dimension nn and the capacity of the reproducing kernel Hilbert space generated by the polynomial kernel.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 173, September 2013, Pages 33–55
نویسندگان
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