کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4608474 1631469 2016 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Digital nets with infinite digit expansions and construction of folded digital nets for quasi-Monte Carlo integration
ترجمه فارسی عنوان
شبکه های دیجیتال با گسترش رقمی بی نهایت و ساخت شبکه های دیجیتالی پیچیده برای ادغام شبه مونت کارلو ؟؟
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی

In this paper we study quasi-Monte Carlo integration of smooth functions using digital nets. We fold digital nets over ZbZb by means of the bb-adic tent transformation, which has recently been introduced by the authors, and employ such folded digital nets as quadrature points. We first analyze the worst-case error of quasi-Monte Carlo rules using folded digital nets in reproducing kernel Hilbert spaces. Here we need to permit digital nets with “infinite digit expansions”, which are beyond the scope of the classical definition of digital nets. We overcome this issue by considering the infinite product of cyclic groups and the characters on it. We then give an explicit means of constructing good folded digital nets as follows: we use higher order polynomial lattice point sets for digital nets and show that the component-by-component construction can find good folded higher order polynomial lattice rules that achieve the optimal convergence rate of the worst-case error in certain Sobolev spaces of smoothness of arbitrarily high order.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 33, April 2016, Pages 30–54
نویسندگان
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