کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4609056 | 1338405 | 2011 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Liberating the dimension for function approximation
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We study approximation of functions that may depend on infinitely many variables. We assume that such functions belong to a separable weighted Hilbert space that is the direct sum of tensor product Hilbert spaces of functions with finitely many variables. The weight sequence γ={γu} is used to moderate the influence of terms depending on finitely many variables from u. We consider algorithms that use finitely many arbitrary linear functionals. Each linear functional is an inner product whose cost depends on the number of active variables of the inner product generator. That is, if the generator has d active variables then the cost is $(d) for a given non-decreasing function $. The error of an algorithm is defined in the worst case setting in a norm given by weighted L2 norms for terms depending on finitely many variables. The ε-complexity is understood as the minimal cost among all algorithms with errors at most ε. We are especially interested in polynomial tractability, where the ε-complexity is bounded by a polynomial in εâ1, and weak tractability, where the ε-complexity is sub-exponential in εâ1. The results are as follows.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 27, Issue 1, February 2011, Pages 86-110
Journal: Journal of Complexity - Volume 27, Issue 1, February 2011, Pages 86-110
نویسندگان
G.W. Wasilkowski, H. Woźniakowski,