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Introduction

  • Gunther Leobacher
  • Friedrich Pillichshammer
Chapter
  • 1.9k Downloads
Part of the Compact Textbooks in Mathematics book series (CTM)

Abstract

In this book we consider the problem of numerical integration over the s-dimensional unit cube [0, 1] s , \(\displaystyle{ \int _{[0,1]^{s}}f(\boldsymbol{x})\,\mathrm{d}\boldsymbol{x} =\int _{ 0}^{1}\cdots \int _{ 0}^{1}f(x_{ 1},\ldots,x_{s})\,\mathrm{d}x_{1}\ldots \,\mathrm{d}x_{s}. }\) Here the dimension s may be large in practical applications. The restriction to integration problems over the unit cube [0, 1] s is mostly for simplicity and in many cases does not impose a big limitation, since most integrals over bounded or unbounded regions can be transformed into integrals over the unit cube (although one has to be careful in choosing suitable transformations which, of course, have influence on the behavior of the transformed integrand).

Keywords

quasi-Monte Carlo (QMC) Equal-weight Quadrature Rules Multivariate Integration Problem Uniform Distribution Modulo Integration Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Gunther Leobacher
    • 1
  • Friedrich Pillichshammer
    • 2
  1. 1.Institute of Financial MathematicsUniversity of LinzLinzAustria
  2. 2.University of LinzLinzAustria

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