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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

The Approximation of Cauchy-Stieltjes and Laplace-Stieltjes Functions

Dietrich Braess and Wolfgang Hackbusch


The treatment of fractional diffusion operators leads to the rational approximation of Cauchy-Stieltjes functions. Similarly the computation of some high-dimensional integrals in quantum chemistry leads to the approximation of Laplace-Stieltjes functions by exponential sums. In both cases the exponential rate of approximation is simply computed via Gauss' arithmetic-geometric iteration and an approximation procedure of the square root function. Surprisingly the convergence rates are different in the two cases although the ways to the two results are very close.

MSC Codes:
41A20, 41A30, 41A25, 65N15, 74M99, 81-08

Related publications

2024 Repository Open Access
Dietrich Braess and Wolfgang Hackbusch

The approximation of Cauchy-Stieltjes and Laplace-Stieltjes functions