Error reduction techniques in quasi-monte carlo integration
نویسندگان
چکیده
منابع مشابه
Error trends in Quasi-Monte Carlo integration
Several test functions, whose variation could be calculated, were integrated with up tp 10 trials using different low-discrepancy sequences in dimensions 3, 6, 12, and 24. The integration errors divided by the variation of the functions were compared with exact and asymptotic discrepancies. These errors follow an approximate power law, whose constant is essentially given by the variance of the ...
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We consider the problem of numerical integration in dimension s, with eventually large s; the usual rules need a very huge number of nodes with increasing dimension to obtain some accuracy, say an error bound less than 10−2; this phenomenon is called ”the curse of dimensionality”; to overcome it, two kind of methods have been developped: the so-called Monte-Carlo and Quasi-Monte-Carlo methods. ...
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In this survey paper we discuss some tools and methods which are of use in quasiMonte Carlo (QMC) theory. We group them in chapters on Numerical Analysis, Harmonic Analysis, Algebra and Number Theory, and Probability Theory. We do not provide a comprehensive survey of all tools, but focus on a few of them, including reproducing and covariance kernels, Littlewood-Paley theory, Riesz products, Mi...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 1999
ISSN: 0895-7177
DOI: 10.1016/s0895-7177(99)00164-8