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[Octave-bug-tracker] [bug #53583] fzero should accept x0 as a scalar

From: Rik
Subject: [Octave-bug-tracker] [bug #53583] fzero should accept x0 as a scalar
Date: Sun, 8 Apr 2018 11:42:10 -0400 (EDT)
User-agent: Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:55.0) Gecko/20100101 Firefox/55.0

Follow-up Comment #3, bug #53583 (project octave):

Octave also accepts a scalar.  See the last part of the documentation from
comment #1:

 If X0 is a single scalar then several nearby and distant values are
 probed in an attempt to obtain a valid bracketing.  If this is not
 successful, the function fails.

The issue is that if you don't give fzero a valid bracketing around the zero
you want it may probe and find a nearby zero instead.  Taking not bessel, but
sin(x) which has zeros at 0, pi, 2*pi, 3*pi, etc.  What value should be
returned for

fzero (@sin, pi/2)

In this case, the algorithm chooses 0, but it could just as well have chosen
the one at pi, or even one further away because the instructions weren't
explicit enough.

I suppose the auto-bracketing mechanism could be re-written.  It's only a few
lines, but because the characteristics of the function are not known we don't
rely on derivatives.


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