论文标题
在减少数位数的数字组件逐个构造的晶格构建集中
On a reduced digit-by-digit component-by-component construction of lattice point sets
论文作者
论文摘要
在本文中，我们研究了一种用于构建加权Korobov类别的准蒙特卡洛集成规则的有效算法。提出的算法是逐数逐数（CBC-DBD）算法的快速组成部分，对于功能空间中的权重表现出足够快的衰减的情况，这对于情况很有用。此处介绍的算法的优点是，如果满足集成的合适假设，计算工作可以独立于要处理的集成问题的维度。新的还原CBC-DBD算法旨在用于构建晶格集集，相应的集成规则（所谓的晶格规则）可用于处理不同类型的功能空间的功能。我们表明，我们的算法构建的集成规则满足了几乎最佳收敛顺序的误差界限。此外，我们提供了有关有效实施的详细信息，以便我们获得以前研究过的先前已知的CBC-DBD算法的大幅加速。数值结果说明了这种改进。
In this paper, we study an efficient algorithm for constructing point sets underlying quasi-Monte Carlo integration rules for weighted Korobov classes. The algorithm presented is a reduced fast component-by-component digit-by-digit (CBC-DBD) algorithm, which useful for to situations where the weights in the function space show a sufficiently fast decay. The advantage of the algorithm presented here is that the computational effort can be independent of the dimension of the integration problem to be treated if suitable assumptions on the integrand are met. The new reduced CBC-DBD algorithm is designed to work for the construction of lattice point sets, and the corresponding integration rules (so-called lattice rules) can be used to treat functions in different kinds of function spaces. We show that the integration rules constructed by our algorithm satisfy error bounds of almost optimal convergence order. Furthermore, we give details on an efficient implementation such that we obtain a considerable speed-up of a previously known CBC-DBD algorithm that has been studied before. This improvement is illustrated by numerical results.
