Abstract
The majorize modelling of the modified Newton method (MNM) is an effective tool for concluding the existence and uniqueness of the solution of nonlinear operator equations. In this paper, we consider MNM together with a new majorant function (MF) that needed weak conditions to solve a nonlinear algebraic system (NLAS). The main advantage of this method is that you only require to establish the inverse of the Jacobian matrix (JM) at the initial guess (IG) and there is no need to compute it at the other iterations. The proposed strategy in this paper is logical and easy to execute. The theorems of MF and convergence are established for the method. Numerical results show that the strategy is efficient and promising.
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