Discrepancy Theory and Quasi-Monte Carlo Integration

被引：24

作者：

Dick, Josef ^{[1
]}

Pillichshammer, Friedrich ^{[2
]}

机构：

[1] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

[2] Univ Linz, Inst Financial Math, A-4040 Linz, Austria

来源：

PANORAMA OF DISCREPANCY THEORY | 2014年 / 2107卷

关键词：

BY-COMPONENT CONSTRUCTION; WEIGHTED L-2 DISCREPANCY; POLYNOMIAL LATTICE RULES; MEAN SQUARES PROBLEM; MULTIVARIATE INTEGRATION; DIGITAL NETS; NUMERICAL-INTEGRATION; STAR-DISCREPANCY; EXPLICIT CONSTRUCTIONS; STRONG TRACTABILITY;

D O I：

10.1007/978-3-319-04696-9_9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this chapter we showthe deep connections between discrepancy theory on the one hand and quasi-Monte Carlo integration on the other. Discrepancy theory was established as an area of research going back to the seminal paper by Weyl [117], whereas Monte Carlo (and later quasi-Monte Carlo) was invented in the 1940s by John von Neumann and Stanislaw Ulam to solve practical problems. The connection between these areas is well understood and will be presented here. We further include state of the art methods for quasi-Monte Carlo integration.

引用

页码：539 / 619

页数：81

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