Integration and approximation based on scramble sampling in arbitrary dimensions

DOI10.1006/jcom.2001.0602zbMath0995.65005OpenAlexW2093213122MaRDI QIDQ1347865

Fred J. Hickernell, Rong-Xian Yue

Publication date: 23 October 2002

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcom.2001.0602

zbMATH Keywords

numerical integrationMonte Carlo methodreproducing kernelworst case settingaverage case settingscramble sampling scheme

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Numerical quadrature and cubature formulas (65D32) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (3)

Strong tractability of integration using scrambled Niederreiter points ⋮ Some current issues in quasi-Monte Carlo methods ⋮ Optimal quadrature for Haar wavelet spaces

Cites Work

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• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• Scrambling Sobol' and Niederreiter-Xing points
• Tractability of multivariate integration for periodic functions
• Tractability of multivariate integration for weighted Korobov classes
• Scrambled net variance for integrals of smooth functions
• On the variance of quadrature over scrambled nets and sequences
• Integration and approximation in arbitrary dimensions
• Ten Lectures on Wavelets
• The asymptotic efficiency of randomized nets for quadrature
• The exponent of discrepancy is at most 1.4778...
• The mean square discrepancy of randomized nets
• Monte Carlo Variance of Scrambled Net Quadrature
• The Mean Square Discrepancy of Scrambled (t,s)-Sequences

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