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Abstract
We describe an adaptive algorithm to compute piecewise sparse polynomial approximations and the integral of a multivariate function over hyper-rectangular regions in medium dimensions. The key ingredient is a quasi-Monte Carlo quadrature rule which can handle the numerical integration of both very regular and less regular functions. Numerical tests are performed on functions taken from Genz package in dimensions up to 5 and on basket options pricing.
Keywords.: Adaptive numerical integration; piecewise polynomial approximations; basket option pricing
Received: 2010-02-05
Revised: 2010-09-21
Published Online: 2010-10-20
Published in Print: 2010-December
© de Gruyter 2010
