Representation of Functions as Walsh Series to Different Bases and an Application to the Numerical Integration of High-Dimensional Walsh Series

DOI10.2307/2153290zbMath0821.42017OpenAlexW2045937166MaRDI QIDQ4317668

Wolfgang Ch. Schmid, Reinhard Wolf, Gerhard Larcher

Publication date: 20 December 1994

Full work available at URL: https://doi.org/10.2307/2153290

zbMATH Keywords

absolute convergencenumerical integration schemePrice systemmultiple generalized Walsh-Fourier series

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Numerical integration (65D30) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (6)

General discrepancy estimates. III: The Erdös-Turán-Koksma inequality for the Haar function system ⋮ On the numerical integration of high-dimensional Walsh-series by quasi-Monte Carlo methods ⋮ Digital nets and sequences constructed over finite rings and their application to quasi-Monte Carlo integration ⋮ Quasi-Monte Carlo methods for numerical integration of multivariate Haar series ⋮ Quasi-Monte Carlo methods for the numerical integration of multivariate Walsh series ⋮ The asymptotic efficiency of randomized nets for quadrature

Cites Work

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• Point sets and sequences with small discrepancy
• Low-discrepancy and low-dispersion sequences
• Orthogonal arrays and other combinatorial aspects in the theory of uniform point distributions in unit cubes
• Good Parameters for a Class of Node Sets in Quasi-Monte Carlo Integration
• On the Numerical Integration of Walsh Series by Number-Theoretic Methods

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