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what is the reliable way to solve a set of nonlinear implict equations without using Jocabian ?

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Lin LI
Lin LI 2013-4-16
I have a nolinear problem ,which is to solve a set of nonlinear implict equations.It is impossible to get the Jocabian of the set of nonlinear eqations since they are implict. what is the reliable way to solve a set of nonlinear implict equations without using Jocabian ? Does Quasi-Newton method work? And how to choose a proper initial value?
If anyone can help, I appreciate it very much.

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