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From: Dion Skordoulis on 25 Feb 2010 21:02
Hello to all,

I'm trying to solve a system of non-linear equations using the Newton's Raphson method. I've created a function which finds the zeros of continuously differentiable function with the use of Jacobian matrices. However, sometimes my initial guess x0 may not be close enough to the true root so the iteration process will never converge to a solution. So, I've created another function where it tries through an iterative process to get f(a)<0 and f(b)>0 in order to approximate the initial guess in the range of [a b]. However, my functions are so complex that in some cases if a c parameter changes may not be able to get the [a b] region properly.

Is there a method that would help me to find a well-behaved region of the root?

I've been also looking for other root-finding methods but i) they are not suitable for a system of equations or ii) you need to define your function as f with a symbolic set of x where in my case this is not possible.

Thanks for any help given.

Dion
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