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We present two new adaptive quadrature routines. Both routines differ frompreviously published algorithms in many aspects, most significantly in how theyrepresent the integrand, how they treat non-numerical values of the integrand,how they deal with improper divergent integrals and how they estimate theintegration error. The main focus of these improvements is to increase thereliability 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 andGautschi and Kahaner. They are shown to be more reliable, albeit in some casesless efficient, than other commonly-used adaptive integrators.

Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants