Lattice rules of minimal and maximal rank with good figures of merit
نویسندگان
چکیده
منابع مشابه
Component-By-Component Construction of Good Intermediate-Rank Lattice Rules
It is known that the generating vector of a rank-1 lattice rule can be constructed component-by-component to achieve strong tractability error bounds in both weighted Korobov spaces and weighted Sobolev spaces. Since the weights for these spaces are nonincreasing, the first few variables are in a sense more important than the rest. We thus propose to copy the points of a rank-1 lattice rule a n...
متن کاملA Note on the Figure of Merit of 2-dimensional Rank 2 Lattice Rules
We give an explicit formula for the figure of merit ρN of 2-dimensional rank 2 lattice rules in terms of continued fractions for rational numbers. Further we generalize Fibonacci lattice rules to rank 2 Fibonacci lattice rules which have the same ratio of the figure of merit to the number of points as the classical Fibonacci lattice rule.
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We develop a fast algorithm for the construction of good rank-1 lattice rules which are a quasi-Monte Carlo method for the approximation of multivariate integrals. A popular method to construct such rules is the component-by-component algorithm which is able to construct good lattice rules that achieve the optimal theoretical rate of convergence. The construction time of this algorithm is O(sn)...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1999
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(99)00220-4