论文标题
创意望远镜进行多款
Creative Telescoping on Multiple Sums
论文作者
论文摘要
我们展示了一系列实用策略的集合，以解决对通过Quasi-Monte Carlo方法得出的积分估计器的分析引起的问题。该问题减少到三重二元总和，从而使我们能够打开自动工具包，该工具包包含诸如创意望远镜之类的工具，可用于推断该总和满足的复发。在应用这些技术时，出现了许多问题，需要手工解决。换句话说，目前没有可以自动解决所有这些问题的创意望远镜实现。因此，我们认为有必要汇编我们尝试的不同策略以及在此过程中遇到的困难。特别是，我们强调了这些计算中证书的必要性，以及其复杂性如何极大地影响计算时间。
We showcase a collection of practical strategies to deal with a problem arising from an analysis of integral estimators derived via quasi-Monte Carlo methods. The problem reduces to a triple binomial sum, thereby enabling us to open up the holonomic toolkit, which contains tools such as creative telescoping that can be used to deduce a recurrence satisfied by the sum. While applying these techniques, a host of issues arose that partly needed to be resolved by hand. In other words, no creative telescoping implementation currently exists that can resolve all these issues automatically. Thus, we felt the need to compile the different strategies we tried and the difficulties that we encountered along the way. In particular, we highlight the necessity of the certificate in these computations and how its complexity can greatly influence the computation time.
