Re: vpasolve to find all real roots for multiple nonlinear equations and multiple variables

[Oliver Heimlich]

Am 31. Mai 2016 02:46:31 MESZ, schrieb sam kjm <address@hidden>:
>I see... Thanks Oliver! I'd try the fsolve from the interval package
>
>
>
>--
>View this message in context:
>http://octave.1599824.n4.nabble.com/vpasolve-to-find-all-real-roots-for-multiple-nonlinear-equations-and-multiple-variables-tp4677276p4677284.html
>Sent from the Octave - General mailing list archive at Nabble.com.
>
>_______________________________________________
>Help-octave mailing list
>address@hidden
>https://lists.gnu.org/mailman/listinfo/help-octave

The interval fsolve function is an excellent option for the problem described 
here. However, its functionality is intimidating if you haven't used interval 
arithmetic before.

Let me give more guidance. 
1, look at the first fsolve example with parameter estimation in the package 
documentation. 
2, exchange the function with your state function f and solve that for f = 0. 
3, The first output argument of fsolve is probably useless in your case. You 
want to plot the second and third output as can be seen in the later examples. 
They will give you a guaranteed inner and outer approximation for the solution 
set.
4, If the approximation isn't accurate enough (e.g. inner approximation is the 
empty set and outer approximation is the whole search range), further knowledge 
of interval analysis is required to fine tune the algorithm and state function. 
You may ping back if you need help with that.

Oliver