2014/04/22 by Josef Dick, Peter Kritzer, Dick, Josef +5
Decision Sciences · Mathematics · Physics and Astronomy · #65D30 #65D32 #Electromagnetic Scattering and Analysis #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1404.5497
openalex publication_date 2014/04/22 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
Lattice rules and polynomial lattice rules are quadrature rules for\napproximating integrals over the s-dimensional unit cube. Since no explicit\nconstructions of such quadrature methods are known for dimensions s > 2, one\nusually has to resort to computer search algorithms. The fast\ncomponent-by-component approach is a useful algorithm for finding suitable\nquadrature rules.\n We present a modification of the fast component-by-component algorithm which\nyields savings of the construction cost for (polynomial) lattice rules in\nweighted function spaces. The idea is to reduce the size of the search space\nfor coordinates which are associated with small weights and are therefore of\nless importance to the overall error compared to coordinates associated with\nlarge weights. We analyze tractability conditions of the resulting QMC rules.\nNumerical results demonstrate the effectiveness of our method.\n