QUADGR

Gauss-Legendre quadrature with Richardson extrapolation.

Description

Yes I know, there is no particular need for another 1-d quadrature.
QUADGK works excellent and the supply on the File Exchange is rich.
Anyway, here is another example.

The quadrature is the 12-point Gauss-Legendre (replace by your favorite).
The error estimate is based on successive interval bisection. Richardson
extrapolation accelerates the convergence for some integrals.

The Richardson extrapolation includes an estimate of the convergence order.
This is necessary for integrals with endpoint singularities. Infinite intervals are
also implemented for completeness.

QUADGR can also be used together with DBLQUAD and TRIPLEQUAD
for double- and triple integrals.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
gaussquad

• MATLAB release: MATLAB 7.5 (R2007b)

[John D'Errico]

Yes, Jonas is correct. The world is not waiting desperately for yet another 1-d quadrature. But this one is a worthy tool to add to your collection. Well written in all respects.