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Quasi-Monte Carlo: A high-dimensional experiment
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Published/Copyright:
May 10, 2014
Abstract
Certain very high-dimensional integrals can be efficiently approximated by quasi-Monte Carlo (q-MC) methods. If the average dimension of the integrand is small, the convergence rate can be near to 1/N, where N is the sample size.
Keywords: Quasi-Monte Carlo; Sobol sequences; high-dimensional
integration; average dimension; mean dimension
MSC: 11K45
The authors recognize the technical assistance of Alex Sobol in preparing this manuscript for publication. The authors are grateful to Michael Milgram and Ronald Davis for their useful suggestions improving the quality of the manuscript.
Received: 2013-12-18
Accepted: 2014-4-20
Published Online: 2014-5-10
Published in Print: 2014-9-1
© 2014 by De Gruyter
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- Quasi-Monte Carlo: A high-dimensional experiment
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Keywords for this article
Quasi-Monte Carlo;
Sobol sequences;
high-dimensional
integration;
average dimension;
mean dimension
Articles in the same Issue
- Frontmatter
- Quasi-Monte Carlo: A high-dimensional experiment
- A spectral method for isotropic diffusion equation with random concentration fluctuations of incoming flux of particles through circular-shaped boundaries
- Multilevel Monte Carlo for Asian options and limit theorems
- Toward a coherent Monte Carlo simulation of CVA
- Field-induced Kosterlitz–Thouless transition in critical triangular-lattice antiferromagnets
