Quasi-Monte Carlo methods for numerical integration of multivariate Haar series

DOI10.1007/BF02510355zbMath0893.65010OpenAlexW4243972486MaRDI QIDQ1378465

Karl Entacher

Publication date: 4 June 1998

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02510355

zbMATH Keywords

numerical integrationlow-discrepancy point setsquasi-Monte Carlo methodsgeneralized Haar functionsintegration error estimates

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Numerical quadrature and cubature formulas (65D32)

Related Items (8)

Unnamed Item ⋮ My dream quadrature rule ⋮ Quasi-Monte Carlo methods for integration of functions with dominating mixed smoothness in arbitrary dimension ⋮ Unnamed Item ⋮ Minimal cubature formulas exact for Haar polynomials ⋮ Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces ⋮ Optimal quadrature for Haar wavelet spaces ⋮ Quasi-Monte Carlo methods for numerical integration of multivariate Haar series. II

Cites Work

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• Point sets and sequences with small discrepancy
• Low-discrepancy and low-dispersion sequences
• General discrepancy estimates. III: The Erdös-Turán-Koksma inequality for the Haar function system
• Quasi-Monte Carlo methods for the numerical integration of multivariate Walsh series
• On the Numerical Integration of Walsh Series by Number-Theoretic Methods
• Representation of Functions as Walsh Series to Different Bases and an Application to the Numerical Integration of High-Dimensional Walsh Series
• Optimal Polynomials for (T,M,S)-Nets and Numerical Integration of Multivariate Walsh Series

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