How can I choose the right numerical solution from NEQNF?

Question

I'm using a function (NEQNF manual page here) which I call using

call neqnf(SYSTEM_OF_EQUATIONS, x, xguess=x_GUESS, itmax = 10000)

where SYSTEM_OF_EQUATIONS is the subroutine that contains equations

f(1)=...x(2)...x(1)...
f(2)=...x(1)...x(4)...
f(3)=...x(3)...x(4)...
f(4)=...x(1)...x(5)...
f(5)=...x(1)...x(5)...

from IMSL libraries on Fortran that lets me to solve a non-linear system with five unknowns in five equations. Because there exists more than one solution (couple of five numbers, real or complex, that solve my system), how can I choose which couple to "use" as solution?

I link an online solver with already entered a piece of my system (only two unknowns in two equations, other variables are constant in this example) which easily show you that there exists more than one solution.

example

To conclude my issue I can say that I have to choose the couple of variables which let other variables to be positive, so an easy check is the way to choose the couple.

Which library function you use? How do you call it? Does the manual tell anything about the solutions? As it stands now, the questions has nothing at all to do with Fortran or even programming. — Vladimir F Героям слава, Jul 15 '15 at 16:38
yes, you are right, I mentioned it only in the title. Now OP contains that info. I know this is not a "pure" programming issue but IMHO it's more a programming issue than a mathematical issue... — mattia.b89, Jul 16 '15 at 07:57
I did not ask just about its name and a link. How do you call it? What did YOU find in the manual about different solutions? — Vladimir F Героям слава, Jul 16 '15 at 07:59

score 1 · Answer 1 · answered Jul 16 '15 at 09:17

1

I don't think the question has anything to do with programming, but I will show how I understand the problem.

You supply an initial guess. Then the method just converges to some solution by a modification of a Newton method.

You can choose the root by the placement of the initial guess. However, the convergence pattern can be very unpredictable (even fractal - https://en.wikipedia.org/wiki/Newton_fractal ) and it may be very difficult to choose the particular root using the initial guess.

answered Jul 16 '15 at 09:17

Vladimir F Героям слава

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this makes me unable to choose wanted solution! – mattia.b89 Jul 16 '15 at 09:31
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That's math. Ask mathematicians to recommend you some otyher method if you think this one is bad... – Vladimir F Героям слава Jul 16 '15 at 09:33

How can I choose the right numerical solution from NEQNF?

1 Answers1