کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4642388 1341341 2008 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Low discrepancy sequences in high dimensions: How well are their projections distributed?
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Low discrepancy sequences in high dimensions: How well are their projections distributed?
چکیده انگلیسی

Quasi-Monte Carlo (QMC) methods have been successfully used to compute high-dimensional integrals arising in many applications, especially in finance. To understand the success and the potential limitation of QMC, this paper focuses on quality measures of point sets in high dimensions. We introduce the order-ℓℓ, superposition and truncation discrepancies, which measure the quality of selected projections of a point set on lower-dimensional spaces. These measures are more informative than the classical ones. We study their relationships with the integration errors and study the tractability issues. We present efficient algorithms to compute these discrepancies and perform computational investigations to compare the performance of the Sobol’ nets with that of the sets of Latin hypercube sampling and random points. Numerical results show that in high dimensions the superiority of the Sobol’ nets mainly derives from the one-dimensional projections and the projections associated with the earlier dimensions; for order-2 and higher-order projections all these point sets have similar behavior (on the average). In weighted cases with fast decaying weights, the Sobol’ nets have a better performance than the other two point sets. The investigation enables us to better understand the properties of QMC and throws new light on when and why QMC can have a better (or no better) performance than Monte Carlo for multivariate integration in high dimensions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 213, Issue 2, 1 April 2008, Pages 366–386
نویسندگان
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