کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4607565 1337869 2011 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Whitney type inequalities for local anisotropic polynomial approximation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Whitney type inequalities for local anisotropic polynomial approximation
چکیده انگلیسی

We prove a multivariate Whitney type theorem for the local anisotropic polynomial approximation in Lp(Q)Lp(Q) with 1≤p≤∞1≤p≤∞. Here QQ is a dd-parallelepiped in RdRd with sides parallel to the coordinate axes. We consider the error of best approximation of a function ff by algebraic polynomials of fixed degree at most ri−1ri−1 in variable xi,i=1,…,d, and relate it to a so-called total mixed modulus of smoothness appropriate to characterizing the convergence rate of the approximation error. This theorem is derived from a Johnen type theorem on equivalence between a certain K-functional and the total mixed modulus of smoothness which is proved in the present paper.


► We proved a multivariate Whitney’s theorem for an anisotropic polynomial approximation.
► Functions to be approximated are defined on a parallelepiped.
► The degrees of polynomials for approximation are fixed but different in each variable.
► Suppose that the size of parallelepiped is going to zero.
► Then the rate of approximation error is estimated by a total mixed modulus of smoothness.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 163, Issue 11, November 2011, Pages 1590–1605
نویسندگان
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