Which is the best method for solving a system of nonlinear equations with more than two variables in each?

Question

Tell from your experience one out of
a) Newton-Raphson
b) Steepest Descent
c) Levenburg-Marquardt
d) Gauss Newton
e) other-please specify

Preferences are that the method should converge and should not take extremely large computation time.

Answer 1

Convergence is a necessity, not a preference. Each method will have convergence criteria differing from the others, so the best choice depends upon the problem - the types of equations.

Answer 2

I have worked a lot with newton-raphson method....it works fine and it is the most famous one...in all the scientific literature i have seen mainly newton-raphson , so i guess it is the convenient and best method

Answer 3

Lagrangean method is also good. u can refer books on mathematical physics. where u find complete answer of question.
this method is lenghthy. newton raphson method is good and easy one. see the book M.L boas or Arfken.

Answer 4

I am only familiar with Grobner basis methods. Probably they are not the most efficient methods as they go for the exact solution rather than approximations.