Two New Methods for Solving Systems of Nonlinear Equations Dr. Nidal E. Hassan

In this paper, we present two new methods for finding
the numerical solutions of systems of the nonlinear equations
F(X)  0 , where n n F :  . The basic idea depend on
founding relationship between minimum of a function and the
solution of systems of the nonlinear equations. The first method
seeks the numerical solution with a sequence of search
directions, which is depended on gradient and Hessian matrix of
function, while the second method is based on a sequence of
conjugate search directions. The study shows that our two
methods are convergent, and they can find exact solutions for
quadratic functions, so they can find high accurate solutions for
over quadratic functions. The purposed two algorithms are
programmed by Mathematica Version9. The approximate
solutions of some test problems are given. Comparisons of our
results with other methods illustrate the efficiency and highly
accurate of our suggested methods.
Key Words: Gradient, Hessian Matrix, Minimization, Nonlinear systems.Conjugate Directions

Assistant Prof, Depart. of Mathematics, Faculty of Science, Al-Baath Universty,
Homes, Syria.


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