[Help-gsl] Re: [A little OT] Algorithm for finding a root / solving an equation

[Vicent]

I partially answer myself:

I've got a copy of the 3rd edition of "Numerical Recipes. The Art of
Scientific Computing", which I've just remembered is an important reference.

Any other suggestion or answer to my post?

Thank you.

--
Vicent Giner


On Tue, Jan 5, 2010 at 14:31, Vicent <address@hidden> wrote:

> Hello.
>
> This is not [only] a specific GSL question, but I think this is a good
> place to put it.
>
> I need to look for the root of a given function. I think that the routines
> described in "gsl_roots.h" feet quite well to my needs, especially those
> called "bracketing algorithms". In fact, I was implementing my own
> "bisection algorithm" before realizing that it is already in GSL and that
> there are also other similar (and faster) alternatives.
>
> In my concrete case, the one-dimensional function whose root I must look
> for is continuous and  strictly increasing, and I can easily find an initial
> interval for any of the bracketing algorithms (I mean, I do know that the
> function has one AND ONLY one root, and I can find a pair of numbers  a  and
>  b  such that  f(a)  differs in sign from  f(b)). Moreover, the derivative
> of my function is difficult to compute, so bracketing algorithms are my
> choice.
>
> My question is not related to those GSL routines, but about other similar
> algorithms. Which other "bracketing" algorithms do you know, for finding the
> root for a one-dimensional continuous monotonic function?? I mean,
> "bisection algorithm" is OK for me, but for example, it is said at the GSL's
> documentation that "Brent-Dekker method" has a faster convergence. So, is
> there any other algorithm with such less than linear convergence, for
> finding roots in a one-dimensional context??
>
> So, my question is NOT about HOW TO compute the root (I could do it with
> Excel's Solver, for example, or with the existing algorithms at the GSL),
> but about which is THE BEST way to do it (and also about how to get profit
> of previous knowledge about my concrete function).
>
> Also, can you recommend some good (on-line or off-line) references about
> numerical algorithms in general to me?? Something like a good and up-to-date
> book or web site with "numerical recipes".
>
> Thank you very much in advance for your patience.
>
> --
> Vicent Giner
>