Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants

Details Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants

2010-06-20

arxiv.org/abs/1006.3962v1

ACM Transactions on Mathematical Software (TOMS), Volume 37 Issue 3, September 2010

Computer Science

Numerical Analysis

32 pages, submitted to ACM Transactions on Mathematical Software

Scientific paper

10.1145/1824801.1824804

We present two new adaptive quadrature routines. Both routines differ from previously published algorithms in many aspects, most significantly in how they represent the integrand, how they treat non-numerical values of the integrand, how they deal with improper divergent integrals and how they estimate the integration error. The main focus of these improvements is to increase the reliability of the algorithms without significantly impacting their efficiency. Both algorithms are implemented in Matlab and tested using both the "families" suggested by Lyness and Kaganove and the battery test used by Gander and Gautschi and Kahaner. They are shown to be more reliable, albeit in some cases less efficient, than other commonly-used adaptive integrators.

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