Component-by-Component Construction of Good Lattice Rules with a Composite Number of Points
نویسندگان
چکیده
منابع مشابه
Component-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 کاملFast component-by-component construction of rank-1 lattice rules with a non-prime number of points
The component-by-component construction algorithm constructs the generating vector for a rank-1 lattice one component at a time by minimizing the worst-case error in each step. This algorithm can be formulated elegantly as a repeated matrixvector product, where the matrix-vector product expresses the calculation of the worst-case error in that step. As was shown in an earlier paper, this matrix...
متن کاملReducing the construction cost of the component-by-component construction of good lattice rules
The construction of randomly shifted rank-1 lattice rules, where the number of points n is a prime number, has recently been developed by Sloan, Kuo and Joe for integration of functions in weighted Sobolev spaces and was extended by Kuo and Joe and by Dick to composite numbers. To construct d-dimensional rules, the shifts were generated randomly and the generating vectors were constructed compo...
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...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2002
ISSN: 0885-064X
DOI: 10.1006/jcom.2002.0650