[Octave-bug-tracker] [bug #37613] Octave precision/accuracy is much lower for quadgk

[Michael Leitner]

Follow-up Comment #28, bug #37613 (project octave):

I thought a bit about an interesting example, but didn't succeed, so now a
trivial example: if you turn on the test, that is, change the line reproduced
below to its intended form
++
if (any (abs (diff (x, [], 2) ./ max (abs (x), [], 2)) < 100 * eps1))
--
then 
++
[a,b]=quadgk (@(x) 1, 1-1e-13, 1)
--
gives an estimate for the integral equal to zero, and also an estimated error
equal to zero. If the test is not active, that is, in the present state of the
code, you can do the integration for as small intervals as you like -- the
estimated value of the integral will be at least in the right order of
magnitude (and within a few eps), only the estimated error is strongly
over-optimistic. But the latter point is another issue, as already 
++
[a,b]=quadgk (@(x) 1, 1-1e-6, 1)
--
claims a precision of 7e20, while in reality it is not more accurate than
eps(1), which perhaps is a consequence of the transformation.


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