Re: [Boost-users] [Math] advice using brent_find_minima()

Subject: Re: [Boost-users] [Math] advice using brent_find_minima()
From: dariomt (dariomt_at_[hidden])
Date: 2014-12-10 09:51:09

John Maddock <boost.regex <at> virgin.net> writes:

> 
> > I'd like to find the root of a function f (find x such that f(x) = 
0).
> >
> > Should I pass abs( f ) to brent_find_minima()?
> 
> No: that's a truly lousy method for finding the root.
> 
> If you have one or more derivatives of f then use 
newton_raphson_iterate 
> or halley_iterate from 
> 
http://www.boost.org/doc/libs/1_57_0/libs/math/doc/html/math_toolkit/inte
rnals1/roots.html
> 
> Otherwise use toms748_solve or bracket_and_solve_root from
> 
> 
http://www.boost.org/doc/libs/1_57_0/libs/math/doc/html/math_toolkit/inte
rnals1/roots2.html. 
>   Note that the latter of these two calls the former, which happens to 
> be asymptotically optimal if you have no derivative information.
> 
> And no, we don't have examples for these as they're "details" that 
> aren't officially part of the library yet.  However, we really should 
do 
> something about that as the code has actually been stable for millennia 
> now 
> 
> HTH, John.
> 

OK, now I got it!
You have brent algorithm for finding the minima, but not brent algorithm 
for finding the root.

I don't have derivative for f, so how does toms748_solve compare to [1]?

Regards

[1] http://en.wikipedia.org/wiki/Brent%27s_method