Component-By-Component Construction of Good Intermediate-Rank Lattice Rules
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...
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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...
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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...
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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 choic...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2003
ISSN: 0036-1429,1095-7170
DOI: 10.1137/s0036142902407162