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From Gilles <gil...@harfang.homelinux.org>
Subject Re: [math] Not using borders in NewtonRaphsonSolver
Date Mon, 05 Aug 2013 12:18:05 GMT
Hello.

On Mon, 05 Aug 2013 15:21:02 +0400, Alexander Nozik wrote:
> Hello,
> I believe it is not a bug but rather some kind of feature, but method
> solve in NewtonRaphsonSolver  does not in fact use the specified
> borders, only middle point. If the root is close to one of borders it
> could eventually go out of the interval. It is not very good
> especially when the function defined only in the specified range.

The class implements the standard algorithm (where the search is not
limited to a bracketing interval). Shortcomings of the method are
described in
   http://en.wikipedia.org/wiki/Newton_Raphson

We already had an occurrence of modifying a standard algorithm (look 
for
the issue concerning "RegulaFalsiSover").
In the above page, there are hints that it would be possible to create
an more robust version of Newton-Raphson; cf.
  
http://en.wikipedia.org/wiki/Successive_over-relaxation#Other_applications_of_the_method
Perhaps, you could experiment with it; and then propose an improvement
on the "dev" ML.

> Additionally it would be got to have ton only f(x)=0 solver but also
> f(x) = a solver. It is easy to transform a function but default 
> method
> for that would be good.

IMHO, this is quite easy to overcome, i.e. by finding the root of
   g(x) = f(x) - a
and does not warrant additional code in Commons Math.


Best,
Gilles


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