On combined component-by-component constructions of lattice point sets
نویسندگان
چکیده
منابع مشابه
On combined component-by-component constructions of lattice point sets
The standard method for constructing generating vectors for good lattice point sets is the componentby-component construction. Numerical experiments have shown that the generating vectors found by these constructions sometimes tend to have recurring components, which can lead to the problem of having projections with all lattice points lying on the main diagonal. In this paper we combine method...
متن کاملComponent-by-component construction of hybrid point sets based on Hammersley and lattice point sets
In a series of recent articles, such as, e.g., [5, 9, 16, 22], point sets mixed from integration node sets in different sorts of quasi-Monte Carlo rules have been studied. In particular, a finite version, based on Hammersley and lattice point sets, was introduced in [16], where the existence of such hybrid point sets with low star discrepancy was shown. However, up to now it has remained an ope...
متن کاملComponent-by-component construction of good lattice rules
This paper provides a novel approach to the construction of good lattice rules for the integration of Korobov classes of periodic functions over the unit s-dimensional cube. Theorems are proved which justify the construction of good lattice rules one component at a time – that is, the lattice rule for dimension s+ 1 is obtained from the rule for dimension s by searching over all possible choice...
متن کاملComponent-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 کاملOn the convergence rate of the component-by-component construction of good lattice rules
We prove error bounds on the worst-case error for integration in certain Korobov and Sobolev spaces using rank-1 lattice rules with generating vectors constructed by the component-by-component algorithm. For a prime number of points n a rate of convergence of the worst-case error for multivariate integration in Korobov spaces of O (n−α/2+δ), where α > 1 is a parameter of the Korobov space and δ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2017
ISSN: 0885-064X
DOI: 10.1016/j.jco.2016.04.001