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Abstract: In this report the behavior of globally adaptive integration algorithms applied to heavily oscillating integrands is examined. Especially the number of integrand evaluations needed to achieve a given accuracy tolerance shows a peculiar dependency on the oscillation's frequency which is explained by mathematical modeling. The mathematical treatment requires Peano constants for Gauss and Gauss-Kronrod integration formulas. For the latter, no general formulas have been derived so far. Mathematica... (Update)
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BibTeX entry: (Update)
@misc{ hlavacs-integrating,
author = "Helmut Hlavacs and Christoph W. Ueberhuber",
title = "Integrating Oscillating Functions",
url = "citeseer.ist.psu.edu/418784.html" }
Citations (may not include all citations):26 A Subroutine Package for Automatic Integration (context) - Piessens, De Doncker et al. - 1983
17 Numerical Integration on Advanced Computer Systems (context) - Krommer, Ueberhuber - 1994
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