Weighted compound integration rules with higher order convergence for all \(N\)

DOI10.1007/s11075-011-9482-5zbMath1240.65002OpenAlexW2138020995MaRDI QIDQ663491

Fred J. Hickernell, Peter Kritzer, Dirk Nuyens, Frances Y. Kuo

Publication date: 15 February 2012

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-011-9482-5

zbMATH Keywords

higher order convergencedigital nets and sequenceslattice rules and sequencesmultivariate integralquasi-Monte-Carlo integration

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Lattices and convex bodies (number-theoretic aspects) (11H06) Integration of real functions of several variables: length, area, volume (26B15) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (7)

Scaled lattice rules for integration on ℝ^{𝕕} achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spaces ⋮ Lattice rules for nonperiodic smooth integrands ⋮ Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation ⋮ Optimal order quadrature error bounds for infinite-dimensional higher-order digital sequences ⋮ Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces ⋮ A constraint on extensible quadrature rules ⋮ MDFEM: multivariate decomposition finite element method for elliptic PDEs with uniform random diffusion coefficients using higher-order QMC and FEM

Uses Software

• QSIMVN

Cites Work

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• A Note on Haselgrove's Method for Numerical Integration
• Extensible Lattice Sequences for Quasi-Monte Carlo Quadrature
• Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces
• Constructing Embedded Lattice Rules for Multivariate Integration

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