The Approximation of Cauchy-Stieltjes and Laplace-Stieltjes Functions

Dietrich Braess () and Wolfgang Hackbusch ()
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Dietrich Braess: Ruhr-Universität Bochum, Mathematisches Institut
Wolfgang Hackbusch: Max-Planck-Institut Mathematik in den Naturwissenschaften

A chapter in Multiscale, Nonlinear and Adaptive Approximation II, 2024, pp 115-143 from Springer

Abstract: Abstract 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 Lebesgue–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 derivations of the two results are very similar.

Date: 2024
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DOI: 10.1007/978-3-031-75802-7_7

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