Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants

Understand

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.