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


From: Vicent
Subject: [Help-gsl] [A little OT] Algorithm for finding a root / solving an equation
Date: Tue, 5 Jan 2010 14:31:10 +0100

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


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