solving nonlinear system of equations

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mona faraji 2011-1-30

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I have a nonlinear system of equations including 2 variables ,and I know that roots are real I tried Newton Raphson method but it is very sensetive to initial conditions and they should be very close to the roots,I also tried fsolve but it gives complex roots for some initial conditions

Is there any way to reduce the sensetivity to initial conditions in Newton Raphson method?I mean a way in which I can choose initial conditions far from roots?

also are there other ways to solve a system of nonlinear equations with real roots except Newton Raphson or fslove?

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Andrew Newell 2011-1-30

By initial condition, do you mean your initial guess for the Newton-Raphson method? By variables, do you mean parameters?

mona faraji 2011-2-3

yes exactally

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Answer 1

Andrew Newell 2011-1-30

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Numerical solutions of nonlinear equations are often sensitive to the initial guess. You may not even be able to determine how many solutions there are. The more you know about the system, the better. How do you know, for example, that the solutions are real?

There are two tricks you might be able to use:

If you can rewrite your system as a polynomial equation, you could use roots.
If you can choose model parameters so you know what the answers are, you could then migrate the solutions to your target problem. This is called homotopy, and the package MATCONT might be useful. You can find it at this address: http://sourceforge.net/projects/matcont/