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MiS Preprint

On the Efficient Computation of High-Dimensional Integrals and the Approximation by Exponential Sums

Dietrich Braess and Wolfgang Hackbusch


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.

Jan 7, 2009
Jan 7, 2009
MSC Codes:
11L07, 41A20
exponential sums, rational functions, Chebyshev approximation, best approximation, completely monotone functions, Heron's algorithm, complete elliptic integrals, Landen transformation

Related publications

2009 Repository Open Access
Dietrich Braess and Wolfgang Hackbusch

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