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Extrapolation and Adaptivity in Software for Automatic Numerical Integration on a Cube

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Abstract

Asymptotic expansions related to the integration of well-behaved functions on simplices and cubes have been known for several decades. Extensions of these results to classes of vertex and line singularities are also known. The nature of these expansions justifies extrapolation using the ε-algorithm of Wynn. In principle this requires a uniform subdivision of the region. This was implemented in QUADPACK for finite intervals and in TRIEX for triangles about 15 years ago. In this paper its incorporation in CUBPACK, a software package for automatic integration over a collection of cubes and simplices, is described and some results are reported. We also report on a special subdivision strategy that offers an alternative approach for higher-dimensional problems.

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  1. Deptarment of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001, Heverlee, Belgium

    Ronald Cools

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Cools, R. Extrapolation and Adaptivity in Software for Automatic Numerical Integration on a Cube. Numerical Algorithms 34, 259–269 (2003). https://doi.org/10.1023/B:NUMA.0000005365.15663.94

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