Quasi--Monte Carlo integration over $\mathbb{R}^d$
نویسندگان
چکیده
منابع مشابه
Quasi–monte Carlo Integration over R
In this paper we show that a wide class of integrals over Rd with a probability weight function can be evaluated using a quasi–Monte Carlo algorithm based on a proper decomposition of the domain Rd and arranging low discrepancy points over a series of hierarchical hypercubes. For certain classes of power/exponential decaying weights the algorithm is of optimal order.
متن کاملMonte-Carlo and Quasi-Monte-Carlo Methods for Numerical Integration
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. ...
متن کاملComputational Higher Order Quasi-Monte Carlo Integration
The efficient construction of higher-order interlaced polynomial lattice rules introduced recently in [6] is considered and the computational performance of these higher-order QMC rules is investigated on a suite of parametric, highdimensional test integrand functions. After reviewing the principles of their construction by the “fast component-by-component” (CBC) algorithm due to Nuyens and Coo...
متن کاملDiscrepancy theory and quasi-Monte Carlo integration
* In this article we show the 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 (1916), 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 conne...
متن کاملError 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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2003
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-03-01569-2