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11.
Jan Baldeaux Josef Dick Gunther Leobacher Dirk Nuyens Friedrich Pillichshammer 《Numerical Algorithms》2012,59(3):403-431
We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such
rules are useful for multivariate quadrature of high-dimensional smooth functions over the unit cube as they achieve the near
optimal order of convergence. The main problem addressed in this paper is to find an efficient way of computing the worst-case
error. A general algorithm is presented and explicit expressions for base 2 are given. To obtain an efficient component-by-component
construction algorithm we exploit the structure of the underlying cyclic group. We compare our new higher order multivariate
quadrature rules to existing quadrature rules based on higher order digital nets by computing their worst-case error. These
numerical results show that the higher order polynomial lattice rules improve upon the known constructions of quasi-Monte
Carlo rules based on higher order digital nets. 相似文献
12.
We consider a GI/GI/1 queue with the shortest remaining processing time discipline (SRPT) and light-tailed service times. Our interest is focused
on the tail behavior of the sojourn-time distribution. We obtain a general expression for its large-deviations decay rate.
The value of this decay rate critically depends on whether there is mass in the endpoint of the service-time distribution
or not. An auxiliary priority queue, for which we obtain some new results, plays an important role in our analysis. We apply
our SRPT results to compare SRPT with FIFO from a large-deviations point of view.
2000 Mathematics Subject Classification: Primary—60K25; Secondary—60F10; 90B22 相似文献
13.
The aim of this paper is to show that one can achieve convergence rates of $N^{-\alpha + \delta }$ for $\alpha > 1/2$ (and for $\delta > 0$ arbitrarily small) for nonperiodic $\alpha $ -smooth cosine series using lattice rules without random shifting. The smoothness of the functions can be measured by the decay rate of the cosine coefficients. For a specific choice of the parameters the cosine series space coincides with the unanchored Sobolev space of smoothness 1. We study the embeddings of various reproducing kernel Hilbert spaces and numerical integration in the cosine series function space and show that by applying the so-called tent transformation to a lattice rule one can achieve the (almost) optimal rate of convergence of the integration error. The same holds true for symmetrized lattice rules for the tensor product of the direct sum of the Korobov space and cosine series space, but with a stronger dependence on the dimension in this case. 相似文献
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