Construction of interlaced polynomial lattice rules for infinitely differentiable functions

DOI10.1007/s00211-017-0882-xzbMath1385.65002arXiv1602.00793OpenAlexW2263105604MaRDI QIDQ2408931

Takashi Goda, Kosuke Suzuki, Josef Dick, Takehito Yoshiki

Publication date: 10 October 2017

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.00793

zbMATH Keywords

convergencenumerical experimentsWalsh functionsfast Fourier transformmultivariate integrationworst-case errorquasi-Monte Carlo algorithmcomponent-by-component construction of lattice point setsfast component-by-component algorithmInterlaced polynomial lattice rulesweighted function space of infinitely differentiable functions

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Monte Carlo methods (65C05) Numerical methods for discrete and fast Fourier transforms (65T50) Random number generation in numerical analysis (65C10) Numerical quadrature and cubature formulas (65D32)

Related Items (4)

Super-polynomial accuracy of one dimensional randomized nets using the median of means ⋮ Approximation of quasi-Monte Carlo worst case error in weighted spaces of infinitely times smooth functions ⋮ A Universal Median Quasi-Monte Carlo Integration ⋮ Efficient multivariate approximation on the cube

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Formulas for the Walsh coefficients of smooth functions and their application to bounds on the Walsh coefficients
• Super-polynomial convergence and tractability of multivariate integration for infinitely times differentiable functions
• Construction of interlaced scrambled polynomial lattice rules of arbitrary high order
• WAFOM over abelian groups for quasi-Monte Carlo point sets
• Low-discrepancy point sets
• Codes for the \(m\)-metric
• Random weights, robust lattice rules and the geometry of the \(cbcrc\) algorithm
• Good interlaced polynomial lattice rules for numerical integration in weighted Walsh spaces
• Proof techniques in quasi-Monte Carlo theory
• Integration in Hermite spaces of analytic functions
• Fast construction of higher order digital nets for numerical integration in weighted Sobolev spaces
• Bounds on Walsh coefficients by dyadic difference and a new Koksma-Hlawka type inequality for quasi-Monte Carlo integration
• Lattice rules for nonperiodic smooth integrands
• A class of generalized Walsh functions
• Exponential convergence and tractability of multivariate integration for Korobov spaces
• Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces
• Explicit Constructions of Quasi-Monte Carlo Rules for the Numerical Integration of High-Dimensional Periodic Functions
• Walsh Spaces Containing Smooth Functions and Quasi–Monte Carlo Rules of Arbitrary High Order
• THE DECAY OF THE WALSH COEFFICIENTS OF SMOOTH FUNCTIONS
• Low-discrepancy point sets obtained by digital constructions over finite fields
• Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations with Random Field Inputs
• Polynomial Lattice Point Sets
• Multivariate integration of infinitely many times differentiable functions in weighted Korobov spaces
• A computable figure of merit for quasi-Monte Carlo point sets
• Hyperbolic cross approximation in infinite dimensions

This page was built for publication: Construction of interlaced polynomial lattice rules for infinitely differentiable functions