کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4609095 | 1338409 | 2010 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Optimal recovery of isotropic classes of twice-differentiable multivariate functions
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Optimal recovery of isotropic classes of twice-differentiable multivariate functions Optimal recovery of isotropic classes of twice-differentiable multivariate functions](/preview/png/4609095.png)
چکیده انگلیسی
We consider the class of functions defined on a convex body in Rd, dâN, whose second derivatives in any direction are uniformly bounded and the class of d-variate functions periodic with respect to a given full-rank lattice L and having uniformly bounded second derivative in any direction. The problem of the optimal algorithm which recovers functions from these classes using their values and values of their gradients at n points (nodes) is considered. We first obtain an estimate for the error of the optimal algorithms with fixed nodes. In the periodic case, for every n sufficiently large, we describe the optimal set of n nodes. When d=2, for certain periodic cases, optimality of the hexagonal arrangement of nodes is shown. For both the periodic case and the non-periodic case we present asymptotic results as n gets large.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 26, Issue 6, December 2010, Pages 591-607
Journal: Journal of Complexity - Volume 26, Issue 6, December 2010, Pages 591-607
نویسندگان
Vladislav F. Babenko, Sergiy V. Borodachov, Dmytro S. Skorokhodov,