[Bug-gsl] One dimensional minimum finding

[Ionut Georgescu]

Hello!

The minimization algorithms quit if the original estimation of the
position of the minimum is not so good, that is if

f(a) > f(x) < f(b)

does not hold.  I find this too hard a condition because even if the
function is monotone, than it still has a minimum, either f(a) or f(b).

But this is not the real reason.  Sometimes it is very difficult to give
a good guess of the minimum, even if we certainly know that there is
one. I tried to improve my guess by running golden_section a few times
before running brent, but it also failed at the above condition, which
is common to all the algorithms.

I would therefore suggest to either remove this condition for algorithms
which are guaranteed to find a minimum, like golden_section, or to
provide a way to circumvent it.

What do you think ?

Thank you,
Ionut

-- 
***************
* Ionuţ Georgescu
* Max-Planck-Institut für Physik komplexer Systeme
* Noethnitzer Str. 38, D-01187 Dresden
* Phone: +49 (351) 871-2209
* Fax:   +49 (351) 871-1999

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