Re: fzero initial bracketing [WAS: bug #31070]

[c.]

On 21 Sep 2010, at 13:58, Jaroslav Hajek wrote:

> Yes, but what attempts? My example algorithm will find the bracketing
> almost always (despite the finite precision), and a simple
> modification can make it always find the bracketing if it exists. It
> may be impractical nevertheless.

whether the algorithm is 'practical' or not depends on how far you  
push it,
what I am trying to propose is something extremely simple which would  
still
have some probability to succeed.
I assume the user is giving his interpretation of the concepts 'far'  
and 'very close'
by specifying the algorithm options and I would like to use those to  
avoid looking
for the bracketing too close or too far away from the initial guess.

Maybe the approaches I have been suggesting do not do this very well,  
but if you are not opposed to the idea of
improving fzero's heuristics alltogether I might keep trying.

> I think a much better (and truly practical) algorithm would not just
> try a number of trial steps, but make use of the function value
> information gathered in the process to attempt to construct "smart"
> trials.

that makes sense, but I'd say the resulting function would be a  
completely
different algorithm than the current fzero.
c.