Self-validating integration and approximation of piecewise analytic functions

Authors:
Knut Petras
Affiliations:
Institut für Angewandte Mathematik, Technische Universität, Pockelsstr. 14, D-38106 Braunschweig, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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Abstract

Let an analytic or a piecewise analytic function on a compact interval be given. We present algorithms that produce enclosures for the integral or the function itself. Under certain conditions on the representation of the function, this is done with the minimal order of numbers of operations. The integration algorithm is implemented and numerical comparisons to non-validating integration software are presented.