Adaptive quadrature method from MATLAB

[ivan-pi]

It would be nice to add the MATLAB algorithm, which is described in

Shampine, L. F. (2008). Vectorized adaptive quadrature in MATLAB. Journal of Computational and Applied Mathematics, 211(2), 131-140. https://doi.org/10.1016/j.cam.2006.11.021

I believe the algorithm is similar to those in QUADPACK, but with a few small differences in how the error estimate is constructed.

For simplicity it offers a unified interface for both proper and improper integrals.

See also

• integral Numerical integration
• quadgk Numerically evaluate integral — Gauss-Kronrod quadrature

[ivan-pi]

Also available in Octave as quadgk.

[holetuananh]

My program shows that it seems with the same absErr and relErr, the Matlab version gives around twice less function evaluations than one from Quadpack. I think that comes from the difference in error estimation (somehow mentioned in Shampine paper).

[jacobwilliams]

• Octave code here: https://github.com/gnu-octave/octave/blob/default/scripts/general/quadgk.m
• Julia code here: https://github.com/JuliaMath/QuadGK.jl/blob/master/src/adapt.jl