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- W3104310777 abstract "A comprehensive overview of lattice rules and polynomial lattice rules is given for function spaces based on `p semi-norms. Good lattice rules and polynomial lattice rules are defined as those obtaining worst-case errors bounded by the optimal rate of convergence for the corresponding function space. The focus is on algebraic rates of convergence O(N−α+ ) for α ≥ 1 and any > 0, where α is the decay of a series representation of the integrand function. The dependence of the implied constant on the dimension can be controlled by weights which determine the influence of the different coordinates. Different types of weights are discussed. The construction of good lattice rules, and polynomial lattice rules, can be done using the same method for all 1 < p ≤ ∞; but the case p = 1 is special from the construction point of view. For 1 < p ≤ ∞ the component-by-component construction and its fast algorithm for different weighted function spaces is then discussed. 1 Lattice rules and polynomial lattice rules The aim is to approximate multivariate integrals over the s-dimensional unit cube" @default.
- W3104310777 created "2020-11-23" @default.
- W3104310777 creator A5045125806 @default.
- W3104310777 date "2014-01-01" @default.
- W3104310777 modified "2023-10-18" @default.
- W3104310777 title "The construction of good lattice rules and polynomial lattice rules." @default.
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