Dear Octave,
Sourceforge user name: dmelliott4550
The submitted routines are described by the demo's texinfo:
## @deftypefn {Function File} {}
integrator_verifier(@var{order},@var{x-lower},@var{x-upper})
## Returns the result of numerically integrating x^order from x-lower
## through x-upper, along with the relative error (Iapprox/Iexact-1)
## for various numbers (from 2 through 10,000) of evenly spaced
## x^order evaluations, including the end points, using the function
## 'integrator.m'.
##
## As can be seen from the results, a function that is 2'nd or 3'rd
## order in x requires at least 3 values. For a 4'th or 5'th, at
## least 5, for a 6'th or 7'th at least 7, for an 8'th or 9'th at
## least 9. While the maximum "exactly" integrated order is the 9'th,
## higher order functions are calculated accurately provided enough
## values are supplied.
##
## Even for "exact" calculations, the relative error in the result is
## often about +/-#.##e-016, due to numerical error, as illustrated
## by the use of the zeroth order.
##
## The function need not be powers of x. With a bit of editing, this
## will test any function. Beware of the relative error in a null
## value.
## @end deftypefn
These routines are both small and fast.
Please find the routines enclosed.
Regards,
Douglas M. Elliott
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