Construction algorithms for polynomial lattice rules for multivariate integration
نویسندگان
چکیده
منابع مشابه
Construction algorithms for polynomial lattice rules for multivariate integration
We introduce a new construction algorithm for digital nets for integration in certain weighted tensor product Hilbert spaces. The first weighted Hilbert space we consider is based on Walsh functions. Dick and Pillichshammer calculated the worst-case error for integration using digital nets for this space. Here we extend this result to a special construction method for digital nets based on poly...
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Recently, generalized digital nets were introduced and shown to achieve almost optimal convergence rates when used in a quasi-Monte Carlo algorithm to approximate high-dimensional integrals over the unit cube. Since their inception, one method of constructing generalized digital nets from classical digital nets has been known. However, the desirable features of generalized digital nets motivate...
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Lattice rules are among the best methods to estimate integrals in a large numberof dimensions. They are part of the quasi-Monte Carlo set of tools. A new class of lattice rules,defined in a space of polynomials with coefficients in a finite field, is introduced in this paper, anda theoretical framework for these polynomial lattice rules is developed. A randomized version isstudi...
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Lattice rules are a family of equal-weight cubature formulas for approximating highdimensional integrals. By now it is well established that good generating vectors for lattice rules having n points can be constructed component-by-component for integrands belonging to certain weighted function spaces, and that they can achieve the optimal rate of convergence. Although the lattice rules construc...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2005
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-05-01742-4