Multidimensional sampling for simulation and integration: Measures, discrepancies, and quasi-random numbers

DOI10.1016/S0010-4655(96)00108-7zbMath0927.65041arXivhep-ph/9606309OpenAlexW3102852010MaRDI QIDQ1295820

F. James, Jiri K. Hoogland, Ronald Kleiss

Publication date: 5 October 1999

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-ph/9606309

zbMATH Keywords

convergencenumerical integrationresearch surveyquasi-Monte Carloquasi-random numberslarge quasi-random point setsquadratic discrepancies

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Random number generation in numerical analysis (65C10) Numerical quadrature and cubature formulas (65D32) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items

Quasi-random integration in high dimensions, Gaussian limits for discrepancies. I: Asymptotic results, Improving the rejection sampling method in quasi-Monte Carlo methods, On scrambled Halton sequences, Statistical properties of generalized discrepancies, SINGINT: automatic numerical integration of singular integrands, On the \(L_2\)-discrepancy for anchored boxes, Quantum field theory for discrepancies, Scaling limits for the Lego discrepancy, Good random number generators are (not so) easy to find

Uses Software

• RANLUX

Cites Work

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• RANLUX: A Fortran implementation of the high-quality pseudorandom number generator of Lüscher
• Monte Carlo integration with quasi-random numbers: Some experience
• Average case complexity of multivariate integration
• Algorithm 659