I'm currently trying to solve a system of (3) nonlinear equations of (3) variables which are the baryonic density, the isospin asymmetry and and the density of a fluid with the Broyden's method (a quasi-Newton method) included in the GSL.

The problem is that I don't know how to avoid negative roots. I don't want them because it's obviously nonphysical. I guess I should use some conditions but I don't know which ones... I'm programming in C.

Could you help please?

Thanks in advance!

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    $\begingroup$ Would Computational Science be a better home for this question? $\endgroup$ – Qmechanic Mar 30 '17 at 10:04
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    $\begingroup$ I'm voting to close this question as off-topic because it is about software design and not physics. Computational Science or Stack Overflow might be better suited. $\endgroup$ – Kyle Kanos Mar 30 '17 at 10:10
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    $\begingroup$ Kinsol, part of the Sundials solver suite (computation.llnl.gov/projects/sundials/kinsol), solves systems of nonlinear algebraic equations, allows you to specify inequality constraints on the variables, and is callable from C. $\endgroup$ – Bill Greene Mar 30 '17 at 16:20
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    $\begingroup$ @nukeguy I'm not sure a Log change of variable is well advised here, as it might lead to poor conditioning. A linear COV might make more sense, though the solution of Bill seems most direct. $\endgroup$ – Spencer Bryngelson Mar 31 '17 at 14:42
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    $\begingroup$ Maybe you should include the system of equations you're solving, for reference? $\endgroup$ – J. M. Apr 1 '17 at 9:13

I finally solved my problem.

I still use the GSL but I changed the Broyden's method for the classical discrete Newton's method because I saw that Broyden's method "is not recommended for serious use" (source: https://www.gnu.org/software/gsl/manual/html_node/Algorithms-without-Derivatives.html#Algorithms-without-Derivatives).

I also programmed "mirrors" to avoid nonphysical values.

Thanks for the assistance.

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