🚀 go-pugleaf

In <1992Dec09.171136.118661@zeus.calpoly.edu>
	mjohnson@zeus.calpoly.edu (Mark S. Johnson) writes:

>You might try adaptive quadrature. In my experience, Romberg is faster
>than adaptive quadrature (can anyone else back this up?)[...]

Not me.  Besides, you can have it both ways.  I remember a subprogram by
Carl de Boor called CADRE, for Cautious ADaptive Romberg Extrapolation.
I think I saw it in a book titled "Mathematical Software" dating from
the *early seventies*.  This is not a cutting edge problem, folks!

The code performs a Romberg integration over the given interval while
monitoring the convergence.  If it fails to reach the theoretical rate,
it divides the interval in two and resumes recursively in each half
(hoping that one of the halves has some sort of singularity but the
other is clean).  It is very effective at isolating sharp peaks, jump
discontinuities and certain endpoint singularities.  I remember passing
it a wrapper that would plot its (x,y) values before returning the
function value (x supplied by CADRE, y returned by some ugly test
function).  The plots were always judiciously graded in the tight spots.

>Adaptive quadrature is best (or at least most easily) implemented as a
>recursive function, so FORTRAN is out. I'm told it CAN be done in
>FORTRAN, but it ain't pretty.

The code in question is in Fortran.
-- 

--Pierre Asselin, Santa Barbara, California
  pa@verano.sba.ca.us