[Scilab-users] root calculation

[Adrien Vogt-Schilb]

On 05/11/2012 14:45, Paul Carrico wrote:
> All,
>
> Thanks for the feedback ...
> ... a basic plot shows the curve is monotonic (see attachment) ; I should plot a 3D curve in order to study the influence of the exponents for example to verify there's one and only one root ...
>
> ... I've to code a fast function to solve this kind of equation ... hundred thousand (and maybe million) of similar equation to solve :-~

hi

beware not to use one single fsolve to solve a set of independent 
equations;

somethign like

function [a b] = f(x,y)
a=x^3 -1
b= y^(0.6456) +4y^.45 - .566
endfunction

fsolve([0 0],f)


this is a bad idea, because fsolve will systematically calculate db/dx 
and da/dy, this would take much longer and much more memory than just 
fsolving x^3 -1, and then y^(0.6456) +4y^.45 - .566
of course this is much worse when you have N outputs and N inputs to 
your function, in this case fsolve calculates N^2 derivatives at each 
step...

>
> That's one of the reasons why I asked about the possible parallelization
>
> Regards
>
> Paul
>
>
>
> -----Message d'origine-----
> De : users-bounces at lists.scilab.org [mailto:users-bounces at lists.scilab.org] De la part de michael.baudin at contrib.scilab.org
> Envoyé : lundi 5 novembre 2012 13:59
> À : International users mailing list for Scilab.
> Objet : Re: [Scilab-users] root calculation
>
> Hi,
>
> This is a nonlinear equation, for which we are searching a zero.
>
> The fsolve function is designed for this purpose:
>
> http://help.scilab.org/fsolve
>
> Notice that there might not be a solution. This is why the algorithm is an optimization problem, where the square norm of f(x) is minimized.
> This method also works for a system of nonlinear equations, so that this is (much) more general than dichotomy, secant, Brent, etc... which are one-variable solvers.
>
> No 1-variable method is available at the Scilab level, to my knowledge.
> But the Brent method is used internally in the computation of the inverse Cumulated Distribution Function (quantile) by the DCDFLIB library (e.g. X=cdfnor("X",Mean,Std,P,Q)). Notice that Matlab has the fzero function :
>
> http://www.mathworks.fr/fr/help/matlab/ref/fzero.html
>
> which uses Brent's method.
> But this method is not available directy in Scilab. This is a good design choice in my opinion, since fsolve is much more general. But I guess that fzero may be faster and more robust, in some cases.
>
> Best regards,
>
> Michaël
>
> Le 2012-11-05 13:13, Paul Carrico a écrit :
>> Dear all,
>>
>> This a stupid question, but how can I solve directly in, Scilab an
>> equation such as :
>>
>> 0.403*X^(-0.121) + 60.5*X^(-0.73) - 0.1839 = 0
>>
>> ?
>>
>> Is-it necessary to code a function ? from memory : dichotomy method,
>> secant method, Brent one etc. ...
>>
>> Regards
>>
>> Paul
>> _______________________________________________
>> users mailing list
>> users at lists.scilab.org
>> http://lists.scilab.org/mailman/listinfo/users
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