Optimal quadrature for Haar wavelet spaces

DOI10.1090/S0025-5718-03-01531-XzbMath1035.65004OpenAlexW2065960076MaRDI QIDQ4433131

Stefan Heinrich, Rong-Xian Yue, Fred J. Hickernell

Publication date: 29 October 2003

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-03-01531-x

zbMATH Keywords

Monte Carlo methodslower boundsquasi-Monte Carlo methodsworst-caseaverage-casehigh dimensional integrationbest asymptotic convergence ratesequi-distribution quadrature rulesmultidimensional Haar wavelet seriesrandom-case

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Numerical methods for wavelets (65T60) Numerical quadrature and cubature formulas (65D32)

Related Items (12)

\(I\)-binomial scrambling of digital nets and sequences ⋮ Strong tractability of integration using scrambled Niederreiter points ⋮ A Monte Carlo Method for Integration of Multivariate Smooth Functions ⋮ My dream quadrature rule ⋮ A construction of polynomial lattice rules with small gain coefficients ⋮ Cubature formulas for function spaces with moderate smoothness ⋮ Quasi-Monte Carlo methods with applications in finance ⋮ Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces ⋮ Embeddings for infinite-dimensional integration and \(L_2\)-approximation with increasing smoothness ⋮ Control variates for quasi-Monte Carlo (with comments and rejoinder) ⋮ Optimal minimax algorithm for integrating fast oscillatory functions in two dimensions ⋮ Discrepancy Theory and Quasi-Monte Carlo Integration

Cites Work

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• Deterministic and stochastic error bounds in numerical analysis
• Quasi-Monte Carlo methods for numerical integration of multivariate Haar series. II
• Scrambling Sobol' and Niederreiter-Xing points
• Base change problems for generalized Walsh series and multivariate numerical integration
• The price of pessimism for multidimensional quadrature
• The microstructure of \((t,m,s)\)-nets
• Integration and approximation based on scramble sampling in arbitrary dimensions
• Scrambled net variance for integrals of smooth functions
• Quasi-Monte Carlo methods for numerical integration of multivariate Haar series
• Average-case analysis of numerical problems
• The discrepancy and gain coefficients of scrambled digital nets.
• On the numerical integration of high-dimensional Walsh-series by quasi-Monte Carlo methods
• Monte Carlo and quasi-Monte Carlo methods in scientific computing. Proceedings of a conference at the University of Nevada, Las Vegas, Nevada, USA, June 23-25, 1994
• Quasi-Monte Carlo methods for the numerical integration of multivariate Walsh series
• On the variance of quadrature over scrambled nets and sequences
• The asymptotic efficiency of randomized nets for quadrature
• On the Numerical Integration of Walsh Series by Number-Theoretic Methods
• The mean square discrepancy of randomized nets
• Monte Carlo Variance of Scrambled Net Quadrature
• The Mean Square Discrepancy of Scrambled (t,s)-Sequences
• Optimal Polynomials for (T,M,S)-Nets and Numerical Integration of Multivariate Walsh Series

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