3 research outputs found
On the subdivision strategy in adaptive quadrature algorithms
AbstractThe subdivision procedure used in most available adaptive quadrature codes is a simple bisection of the chosen interval. Thus the interval is divided in two equally sized parts. In this paper we present a subdivision strategy which gives three nonequally sized parts. The subdivision points are found using only available information. The strategy has been implemented in the QUADPACK code DQAG and tested using the “performance profile” testing technique. We present test results showing a significant reduction in the number of function evaluations compared to the standard bisection procedure on most test families of integrands
Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants
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.Comment: 32 pages, submitted to ACM Transactions on Mathematical Softwar