کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5774763 1413566 2017 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Quasi-Monte Carlo integration for twice differentiable functions over a triangle
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Quasi-Monte Carlo integration for twice differentiable functions over a triangle
چکیده انگلیسی
We study quasi-Monte Carlo integration for twice differentiable functions defined over a triangle. We provide an explicit construction of infinite sequences of points including one by Basu and Owen (2015) as a special case, which achieves the integration error of order N−1(log⁡N)3 for any N≥2. Since a lower bound of order N−1 on the integration error holds for any linear quadrature rule, the upper bound we obtain is best possible apart from the log⁡N factor. The major ingredient in our proof of the upper bound is the dyadic Walsh analysis of twice differentiable functions over a triangle under a suitable recursive partitioning.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 454, Issue 1, 1 October 2017, Pages 361-384
نویسندگان
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