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• W1938947360 abstract "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), or O(sn) when using O(n) memory, for an s-dimensional lattice rule with n points. We show how to construct good lattice rules in time O(sn log(n)), using O(n) memory, by means of a new algorithm, called the fast component-by-component algorithm. First this is shown for the base case when n is a prime number and the underlying function space is a weighted, shift-invariant and tensor-product reproducing kernel Hilbert space. Then we show that, by a minor increase in construction cost, also more generally weighted function spaces can be handled by the fast algorithm. In particular we show this for order-dependent weights. When n is not a prime number it turns out that fast construction is also possible, although the construction is more involved for numbers n which have a large number of unique prime factors. An additional advantage is obtained when choosing n to be a prime power, since then the rules are embedded for increasing powers of the prime. Using this embedding, we propose a new fast algorithm to construct lattice sequences which can be used point by point. Two natural extensions of the algorithm are the construction of polynomial lattice rules and so called copy rules. We show that also here the fast componentby-component algorithm can be applied. The quality of the constructed point sets is finally demonstrated on some finance and statistics examples." @default.
• W1938947360 created "2016-06-24" @default.
• W1938947360 creator A5045125806 @default.
• W1938947360 date "2007-04-21" @default.
• W1938947360 modified "2023-09-23" @default.
• W1938947360 title "Fast construction of good lattice rules" @default.
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• W1938947360 cites W134944766 @default.
• W1938947360 cites W1496801598 @default.
• W1938947360 cites W1510478584 @default.
• W1938947360 cites W152683667 @default.
• W1938947360 cites W1565176583 @default.
• W1938947360 cites W1590281894 @default.
• W1938947360 cites W163969975 @default.
• W1938947360 cites W1966582744 @default.
• W1938947360 cites W1966904279 @default.
• W1938947360 cites W1971362449 @default.
• W1938947360 cites W1976544585 @default.
• W1938947360 cites W1978759179 @default.
• W1938947360 cites W1981663184 @default.
• W1938947360 cites W1981743146 @default.
• W1938947360 cites W1985018928 @default.
• W1938947360 cites W1986280275 @default.
• W1938947360 cites W1987517531 @default.
• W1938947360 cites W1989439787 @default.
• W1938947360 cites W2000834181 @default.
• W1938947360 cites W2004971474 @default.
• W1938947360 cites W2008619479 @default.
• W1938947360 cites W2011200438 @default.
• W1938947360 cites W2015558767 @default.
• W1938947360 cites W2017001763 @default.
• W1938947360 cites W2021578090 @default.
• W1938947360 cites W2027669629 @default.
• W1938947360 cites W2029946422 @default.
• W1938947360 cites W2031141876 @default.
• W1938947360 cites W2034638017 @default.
• W1938947360 cites W2035455944 @default.
• W1938947360 cites W2040396531 @default.
• W1938947360 cites W2041165402 @default.
• W1938947360 cites W2042083287 @default.
• W1938947360 cites W2043419861 @default.
• W1938947360 cites W2043466875 @default.
• W1938947360 cites W2044248217 @default.
• W1938947360 cites W2048236567 @default.
• W1938947360 cites W2048312356 @default.
• W1938947360 cites W2054312661 @default.
• W1938947360 cites W2059141990 @default.
• W1938947360 cites W2061750459 @default.
• W1938947360 cites W2062216289 @default.
• W1938947360 cites W2067942429 @default.
• W1938947360 cites W2076120296 @default.
• W1938947360 cites W2076760134 @default.
• W1938947360 cites W2078197553 @default.
• W1938947360 cites W2079366547 @default.
• W1938947360 cites W2080608516 @default.
• W1938947360 cites W2080686387 @default.
• W1938947360 cites W2084898049 @default.
• W1938947360 cites W2084937640 @default.
• W1938947360 cites W2086574596 @default.
• W1938947360 cites W2092549287 @default.
• W1938947360 cites W2093425374 @default.
• W1938947360 cites W2093625674 @default.
• W1938947360 cites W2094199988 @default.
• W1938947360 cites W2095595785 @default.
• W1938947360 cites W2096070062 @default.
• W1938947360 cites W2101589741 @default.
• W1938947360 cites W2124827273 @default.
• W1938947360 cites W2137224975 @default.
• W1938947360 cites W2140262981 @default.
• W1938947360 cites W2145169372 @default.
• W1938947360 cites W2148876995 @default.
• W1938947360 cites W2155817197 @default.
• W1938947360 cites W2160346753 @default.
• W1938947360 cites W2166634029 @default.
• W1938947360 cites W2170219930 @default.
• W1938947360 cites W2183868163 @default.
• W1938947360 cites W2228579993 @default.
• W1938947360 cites W2337737559 @default.
• W1938947360 cites W2499620708 @default.
• W1938947360 cites W2521511653 @default.
• W1938947360 cites W2523347533 @default.
• W1938947360 cites W2798909945 @default.
• W1938947360 cites W2801179766 @default.
• W1938947360 cites W3135037104 @default.
• W1938947360 cites W39759813 @default.
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• W1938947360 hasPublicationYear "2007" @default.
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