FoCM 2014 conference

Workshop B5 - Information Based Complexity - Semi-plenary talk

December 16, 14:35 ~ 15:25 - Room B23

## Numerical Integration

### Josef Dick

### The University of New South Wales, Australia - josef.dick@unsw.edu.au

In this talk we discuss various results on numerical integration for functions defined on a domain $D \subseteq \mathbb{R}^d$. In quasi-Monte Carlo theory one considers the domain $[0,1]^s$. In this case one wants quadrature points which are well distributed. If the dimension is large this can be a challenging problem. Another problem which often occurs is that the domain is not the unit cube (a standard example is $\mathbb{R}^s$). In this case one can either use some transformation to obtain an integral over the unit cube or construct quadrature rules in the given domain. Applications of such integration techniques include option pricing, the estimation of the expectation value of solutions of PDEs with random coefficients and some problems from machine learning.

Joint work with Christoph Aistleitner (JKU Linz, Austria), Johann Brauchart (TU Graz, Austria), Takashi Goda (University of Tokyo, Japan), Peter Kritzer (JKU Linz, Austria), Frances Kuo (UNSW, Australia), Gunther Leobacher (JKU Linz, Austria), Quoc Thong Le Gia (UNSW, Australia), Dirk Nuyens (KU Leuven, Belgium), Friedrich Pillichshammer (JKU Linz, Austria), Christoph Schwab (ETH Z\"urich, Switzerland), Kosuke Suzuki (University of Tokyo, Japan), Takehito Yoshiki (University of Tokyo, Japan) and Houying Zhu (UNSW, Australia).