Principles of verified numerical integration

Authors:
Knut Petras
Affiliations:
Institute for Computational Mathematics, TU Braunschweig Pockelsstrasse, Braunschweig, Germany
Venue:
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Year:
2007

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Abstract

We describe methods for the numerical calculation of integrals with verified error bounds. The problems range from integration over an interval to integration of parameter-dependent integrands over the whole d-variate space. It is argued, why we use bounds for the integrands in the complex plane as a tool for bounding the error in our own integration software.