Discrepancy-based error estimates for quasi-Monte Carlo. I: General formalism

DOI10.1016/0010-4655(96)00084-7zbMath0926.65027arXivhep-ph/9601270OpenAlexW3105588780MaRDI QIDQ1294646

Ronald Kleiss, Jiri K. Hoogland

Publication date: 25 August 1999

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

Full work available at URL: https://arxiv.org/abs/hep-ph/9601270

zbMATH Keywords

error estimatequasi-Monte Carlo methodmeasure of (non)uniformitynumerical multidimensional integration

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Numerical quadrature and cubature formulas (65D32)

Related Items (7)

Gaussian limits for discrepancies. I: Asymptotic results ⋮ Asymptotic properties of the spectral test, diaphony, and related quantities ⋮ Statistical properties of generalized discrepancies ⋮ Quantum field theory for discrepancies ⋮ Quantum field theory for discrepancies. II: \(1/N\) corrections using fermions ⋮ Discrepancy-based error estimates for quasi-Monte Carlo. III: Error distributions and central limits ⋮ Discrepancy-based error estimates for quasi-Monte Carlo. II: Results in one dimension

Cites Work

• On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
• Discrepancy and integration of continuous functions
• Monte Carlo integration with quasi-random numbers: Some experience
• Average case complexity of multivariate integration
• Algorithm 659
• Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators
• On irregularities of distribution
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