Approximation of High-Dimensional Numerical Problems - Algorithms, Analysis and Applications (15w5047)


(University of Waterloo)

(University of New South Wales)

Henryk Wozniakowski (Columbia University)


The Banff International Research Station will host the "Approximation of High-Dimensional Numerical Problems - Algorithms, Analysis and Applications" workshop from September 27th to October 2nd, 2015.

High-dimensional problems occur in many scientific disciplines. They arise for various reasons, including the analysis of data in which each sample is defined by the measurement of hundreds of different quantities or the use of models that are based on a large number of random or deterministic variables. When dealing with high-dimensional problems, it is rarely possible to obtain exact solutions. One must then resort to numerical methods. A further complication is that for these problems traditional numerical and other methods are often not feasible. This is due to a phenomenon called the curse of dimensionality, which refers to the problem that occurs when the number of information operations (e.g, function evaluations) grows exponentially fast with the dimension of the problem.

Fortunately, some high-dimensional problems that arise in practice have a structure that allows specialized numerical methods that are able to cope with large dimensions. These specialized methods -- which include quasi-Monte Carlo and sparse-grid methods -- have seen a spectacular flowering in the last decade. They are used on a wide range of applications such as finance, physics, climate modelling, geomechanics, etc. The goal of this workshop is to bring together researchers working on theoretical and practical aspects of these methods, so that they can exchange information on recent findings, and find solutions to the challenges that prevent theoretical advances from being applied in practice.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).