[Octave-bug-tracker] [bug #60539] Slow performance of betaincinv.m

[Rik]

Follow-up Comment #5, bug #60539 (project octave):

After some testing I find that the Newton's method doesn't converge well for
some values of X, A, and B.  I suppose this was why the two-step process was
used where the initial 10 bisection steps placed the trial position x0 in a
region where the Newton's Method process was quadratic in convergence.

My first thought is to go back to the two-step approach, but rather than a
fixed 10 iterations of bisection, use some other threshold such as closeness
of objective function to 0.  Once Octave was reasonably close then switch over
to the Newton's Method which in my testing did converge quickly when in range
of the solution.

Alternatively, a more complex solver might be written along the lines of
fzero() which decides on a step-by-step basis whether to pursue a Newton step
or a bisection step.


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