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

[Michael Leitner]

Follow-up Comment #17, bug #60539 (project octave):

I reported the problem with betainc as bug #60682.

You did understand correctly what I had written, but I was in error. The case
with lost accuracy would have been for alpha=1/4, but in this case I see that
the initial value is so good that it does not need to iterate at all (so after
the first step it has converged, no matter what the stopping criterion).
However, where your stopping criterion is unnecessarily inaccurate is just for
small y: with alpha=2 and beta=1, betainc is just x^2, so betaincinv is just
sqrt(y). My stopping criteria, both the original one as well as the one I
suggested in comment #15 and attach here as newbeta2.m give the correct result
1e-20 for x=1e-40, while your implementation gives 2.22e-16. Yes, on an
absolute level this is correct to eps(1) (it practically is eps(1)), but on a
relative level it is inaccurate by a factor 10000. 


y=1e-40;



(file #51491)
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Additional Item Attachment:

File name: newbeta2.m                     Size:9 KB
    <https://file.savannah.gnu.org/file/newbeta2.m?file_id=51491>



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