Re: limiting the range of solutions with fsolve

[Sergei Steshenko]

----- Original Message -----
> From: wwwups <address@hidden>
> To: address@hidden
> Cc: 
> Sent: Wednesday, October 31, 2012 9:29 PM
> Subject: limiting the range of solutions with fsolve
> 
> All,
> 
> I am a bit of a newbie to Octave, and have been using it to solve sets of
> (highly) non-linear equations with 2 or 3 variables. I know that all three
> variables (x1, x2, x3)  lie within -1 to 1. How can I limit the solutions to
> this range?
> 
> Thanks!
> 
> 
> 


It is not an Octave question, it's a general math question.

You need to solve

F(x1, x2, x3) = 0;

Convert your task to solving

F(f(X1), f(X2), f(X3)) = 0;

and choose the 'f' function such that

f(+Inf) == 1
f(-Inf) == -1
.

Then, having found a solution in terms of unconstrained X1, X2, X3 get back to 
your original variables:

x1 = f(X1);
x2 = f(X2);
x3 = f(X3);
.

A trivial choice for 'f' is for you case is:

f(X) = 2 * atan(X) / pi
.

Regards,
  Sergei.