正交群和Grassmannian流形上的一致分布序列
Uniformly distributed sequences in the orthogonal group and on the Grassmannian manifold
摘要：
近几十年来，拟蒙特卡罗方法方法在数值分析的许多领域取代了经典的蒙特卡罗方法。本文的目的是将拟蒙特卡罗方法推广到一个新的方向。我们构造并实现了一个在正交群中的均匀分布序列。从这个序列中，我们得到一个均匀分布的序列上的格拉斯曼流形$G(n,k)$，我们用它来近似积分几何公式。我们表明，我们的算法相比，以及与经典的随机结构，因此，激励未来的研究的各个方向。
英文摘要：
Quasi-Monte Carlo methods replaced classical Monte Carlo methods in many areas of numerical analysis over the last decades. The purpose of this paper is to extend quasi-Monte Carlo methods into a new direction. We construct and implement a uniformly distributed sequence in the orthogonal group O(n). From this sequence we obtain a uniformly distributed sequence on the Grassmannian manifold $G(n,k)$, which we use to approximate integral-geometric formulas. We show that our algorithm compares well with classical random constructions and, thus, motivate various directions for future research.
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