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[Octave-bug-tracker] [bug #37613] Octave precision/accuracy is much lowe

From: David Bateman
Subject: [Octave-bug-tracker] [bug #37613] Octave precision/accuracy is much lower for quadgk
Date: Wed, 24 Oct 2012 22:05:39 +0000
User-agent: Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:16.0) Gecko/20100101 Firefox/16.0

Follow-up Comment #2, bug #37613 (project octave):

In fact if you replaced h0 with h you'd also have to replace trans(subs) with
subs. As for the sense of the comment, I believe I based it on the statement
in section section of the Shampine paper

We break off the computation if arguments become closer in a relative sense
than 100 times the unit roundoff eps. This is not entirely straightforward
because of the transformations: The test must be done after the variable t
in the formulas is transformed to the variable x given to the function f (x)
there are four sets of transformations. 

The paper itself can be found at 


and I didn't have any other reasons for this comment. However changing line
322 of quadgk to read

if (any (abs (diff (subs, [], 2) / h) < 100 * myeps))

then running "test quadgk" passes all of the tests. These tests include tests
for infinite bounds and singular integrands and so probably give a pretty
clear indication that such a change would be acceptable, even if Shampine
himself didn't recommend it. Perhaps Mathworks modified this behavior after
the inclusion of quadgk in Matlab?



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