Elisabeth Larsson, Researcher at Uppsala University
Radial basis function approximations for high-dimensional PDEs
Radial basis function methods have some properties that make them attractive for approximation of functions in many dimensions or solutions to high-dimensional PDE problems. Application areas where such problems arise are e.g. financial mathematics, quantum dynamics, and molecular biology. In this presentation, we show how some of the RBF advantages can be exploited to reduce computational cost and memory requirements in order to make computations in n>3 dimensions feasible. We show numerical results for pricing of European basket options in one, two, and three dimensions. Compared with an adaptive finite difference method, the RBF method is an order of magnitude faster and has similar memory requirements. However, we believe that further improvements are possible and we give some ideas about future directions of research.
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Name: Ian Cunningham