کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4607565 | 1337869 | 2011 | 16 صفحه PDF | دانلود رایگان |

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.
Journal: Journal of Approximation Theory - Volume 163, Issue 11, November 2011, Pages 1590–1605