PANUMIWAL: a System for the Parallel Numerical Integration of High-Dimensional Functions

PANUMIWAL is a system for the parallel numerical integration of high-dimensional functions based on number-theoretical methods. We describe the state of the art of this system and we describe projected work concerning this system. 1 Introduction In a series of papers by the last two authors and several co-authors, a theoretical method for the numerical integration of high-dimensional functions, based on number-theoretical methods was developed in detail. See for example [7], [4], [5], [6], [3], [1], [2], and [8]. This method is called "digital lattice rule" and essentially is based on the use of a new class of highdimensional, extremely well distributed, number-theoretical point sets in an s-dimensional unit cube. Recently, we have implemented this theoretical method and at the moment we can provide an already highly efficient system for the parallel numerical integration of functions. We call this sytem PANUMIWAL for PArallel NUMerical Integration of WALsh series. Work on this system..