The real issue here is what is "tol" supposed to mean? The quadndg
documentation simply calls it a tolerance parameter.
The existing quadndg is relative tolerance=tol, absolute tolerance=0; as
you correctly observe, an absolute tolerance of 0 means integrals with a
value of 0 have no tolerance at all, and hence never converge.
Your proposed change is relative tolerance=tol, absolute tolerance=tol.
The 1D quad in core Octave makes tol a vector, and uses relative
tolerance=tol(2), absolute tolerance=tol(1). This would also be easy to
implement: if ( norm(int_old-int) < max(norm(int.*tol(2)),abs(tol(1)))
Note that this will give an error with a 1-element tol, to avoid this
add if(length(tol)!=2);tol=[0 tol];endif (for compatibility with
existing code) or if(length(tol)!=2);tol=[tol tol];endif (possibly what
1d quad does, as quad('sin',0,2*pi,1) doesn't give an error but
quad('sin',0,2*pi,[0 1]) does) to the beginning of the function.
I don't know what MATLAB does, or if it even has an equivalent function.
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