Algorithm 691: improving QUADPACK automatic integration routines

Two automatic adaptive integrators from QUADPACK (namely, QAG and QAGS) are modified by substituting the Gauss-Kronrod rules used for local quadrature with recursive monotone stable (RMS) formulas. Extensive numerical tests, both for one-dimensional and two-dimensional integrals, show that the resulting programs are faster, perform less functional evaluations, and are more reliable.