| Summary: | The prominent method for solving nonlinear systems of equations is the Newton method, unfortunately this method do have some shortcomings, these includes computation of the Jacobian matrix, solving the Newton system in every iteration, computing and storing an n x n matrix at each iteration which may be difficult, computationally expensive or even impossible to compute for large scale problems. Numerous research and modifications have been done recently to improve the efficiency of these methods. To overcome such drawbacks, a research work is proposed, titled "A Family of CG-Type Methods via Quasi-Newton Updates for Solving Symmetric Systems of Nonlinear Equations". This is done successfully by modifying the classical SRI (Symmetric Rank One), DFP (Davidon-Fletcher-Powell), Broyden and PSB (Powell Symmetric Broyden) updates. The attractive attribute of these methods are simple implementation and derivative free approach, thereby require low memory storage. The computational experiment is based on number of iterations, CPU time and residual norm of F(Xk)' The code for the methods was done using MATLAB 7.1, R2009b programming environment and run on a personal computer 2.4GHz, Intel (R) Core (TM) i7-5500U CPU processor, 4GB RAM memory and on windows XP operator in order to check its efficiency and robustness. For every test problem, different initial points with different dimensions are used, the numerical results are analyzed using the performance profile introduced in Dolan and More. By solving several benchmark problems, the proposed methods are compared with their classical counterparts. The numerical results demonstrate that the proposed methods are fast in terms of CPU time, efficient in terms of number of iterations and effective in approximating the solution. The global convergence properties of the proposed methods are established under appropriate conditions.
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