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MiS Preprint
3/2009
On the Efficient Computation of High-Dimensional Integrals and the Approximation by Exponential Sums
Dietrich Braess and Wolfgang Hackbusch
Abstract
The approximation of the functions $1/x$ and $1/\sqrt x$ by exponential sums enables us to evaluate some high-dimensional integrals by products of one-dimensional integrals. The degree of approximation can be estimated via the study of rational approximation of the square root function. The latter has interesting connections with the Babylonian method and Gauss' arithmetic-geometric process.
On the efficient computation of high-dimensional integrals and the approximation by exponential sums
In: Multiscale, nonlinear and adaptive approximation : dedicated to Wolfgang Dahmen on the occasion of his 60th birthday / Ronald A. DeVore... (eds.) Berlin [u.a.] : Springer, 2009. - pp. 39-74
