Using Trust Region Method with BFGS Technique for Solving Nonlinear Systems of Equations

Abstract

Abstract The major aim of this paper is to find a solution for systems of non-linear equations, a new method is suggested by combining the trust region method (TRM) with BFGS technique, which will help us to find the solution of the non-linear system in less time and less effort, by using BFGS in a new equation based on [Xiangrong Li, Bopeng Wang & Wujie Hu]. Then the convergence of the new algorithm was provided and also calculate the numerical results. By comparing the suggested method with three other methods in terms of time, functions evaluation and number of iterations, the numerical result will tell us that our method is the best.