Quasi-Monte Carlo Software

Speaker:

Fred Hickernell, professor of mathematics, Illinois Institute of Technology

Description:

Quasi-Monte Carlo (QMC) methods achieve substantial efficiency gains by replacing independent and identically distributed (IID) random points by low discrepancy (LD) points.  LD point generators and QMC algorithms are active research areas.  Practitioners are attracted to QMC by the promise of  efficiency gains.

This tutorial highlights several readily available QMC software libraries in various languages.  We describe the components of a QMC calculation:  the LD point generators, problem specification, methods for speeding up the computation, and stopping criteria.  We argue that excellent QMC software requires the collaboration of a community---not only the efforts of individual research groups.  

During this tutorial we provide hands-on experience with QMCPy, a Python 3 library that draws on the work of several experts.  We do this through the Google Colaboratory notebook at https://tinyurl.com/QMCPyTutorial.  Minimal experience with QMC or Python is assumed.

Bio:  Fred Hickernell received his PhD from Massachusetts Institute of Technology.  He served on the faculty of University of Southern California and Hong Kong Baptist University before joining Illinois Institute of Technology in 2005.  His research focuses on adaptive algorithms for multivariate integration and function approximation.  He works on both the theory and the software sides.

Computational Mathematics & Statistics