An evaluation of Clenshaw-Curtis quadrature rule for integration w.r.t. singular measures

Authors:
F. Calabrò;A. Corbo Esposito
Affiliations:
DAEIMI & LAN, Universitíí degli Studi di Cassino, Via G. Di Biasio 43, I-03043 Cassino (FR), Italy;DAEIMI & LAN, Universitíí degli Studi di Cassino, Via G. Di Biasio 43, I-03043 Cassino (FR), Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

This work is devoted to the study of quadrature rules for integration with respect to (w.r.t.) general probability measures with known moments. Automatic calculation of the Clenshaw-Curtis rules is considered and analyzed. It is shown that it is possible to construct these rules in a stable manner for quadrature w.r.t. balanced measures. In order to make a comparison Gauss rules and their stable implementation for integration w.r.t. balanced measures are recalled. Convergence rates are tested in the case of binomial measures.