Whatever method you use, I would suggest to verify your result, because all
those methods are iterative and may "think" they succeed, due to round-off
errors or otherwise. So verifying the result returned is always a good idea,
and besides it's easy to do that. For example:
load(mnewton)$
equs:[x1-x2^4+x3-5,x1^2+x2^3-3,x1+x2*x3^2]$
sol:mnewton(equs,[x1,x2,x3],[2,1,2]);
gives
[[x1 = 1.733285742377482, x2 = - 0.16235405884328, x3 = 3.267409046090958]]
which is correct, as we can easily verify:
ev(equs,sol);
[0.0, 4.5970172113385388E-16, - 4.4408920985006262E-16]
2011/9/13 Raymond Toy <toy.raymond at gmail.com>
> In addition, there is lbfgs and minpack_solve for doing unconstrained
> minimization. If you can express your problem as a minimization problem,
> then these two routines (and minpack_lsquares) might be useful.
>
> Ray
>
>
>
> On Mon, Sep 12, 2011 at 3:51 PM, Panagiotis Papasotiriou <
> p.j.papasot at gmail.com> wrote:
>
>> Yes, Bernando, it is possible. Have a look at the package mnewton. It
>> implements a multivariate Newton method for solving systems of non-linear
>> differential equations. That is, it is a generalization of the
>> Newton-Raphson method for root-finding of functions of one variable.
>> Personally, I would prefer Broyden's method instead of multivariate
>> Newton, because Broyden's method is based on Secant (its one-dimension
>> equivalent). Nevertheless, multivariate Newton is not bad.
>> Note that, depending on the problem at hand, a "good" initial guess might
>> be necessary. If your initial guesses for the unknown variables are very
>> bad, mnewton will fail to converge, and you will need to try again with
>> different guesses.
>>
>> 2011/9/12 bernardo gomez <bernardo at fceia.unr.edu.ar>
>>
>>> Hi !
>>> It is possible to solve numerically a system Maxima of 2 nonlinear
>>> equations ?
>>> Thanks !
>>> bernardo
>>> --
>>>
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>>
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>