Could somebody who knows well the method of numerical solutions of system of nonlinear algebraic equations nonlinear algebraic equations recommand a global convergence methods? thank you very much!
Without derivatives the methods are typically less effective (can be 'inefficient' real quick, if it's possible to apply in your case methods utilizing gradients they are typically far more usable & efficient), but ones like the simplex method and conjugate direction methods are zeroth order methods and as such don't use gradients. The simplex method is pretty used for example in unconstrained nonlinear optimization.
For a system of nonlinear algebraic equations, if you want to find all the solutions, you can also consider the continuation method (some people call it homotopy continuation method).
Here is one link: http://www.math.uic.edu/~jan/PHCpack/phcpack.html
Chingkui, my equations is not the polynomial. it contains the hyperbolic functions and is diffificult to simpilify to hyperbolic functions. how can I do with homotopy continuation method?