HYBRIDIZATION OF A MATRIX-FREE METHOD VIA DOUBLE STEP LENGTH APPROACH WITH MULTI-STEP ALGORITHM FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS.

Authors

System of Nonlinear Equations, Acceleration parameter, Multi- step iterative scheme, Jacobian Matrix, Global convergence.

This paper introduces a novel hybrid method that integrates a matrix- free approach with a double step length strategy

and a multi-step iterative process, aimed at effectively solving large-scale systems of nonlinear equations. By deriving an

acceleration parameter through the first-order Taylor series expansion, we approximate the Jacobian matrix, thereby

enhancing the convergence of the proposed method. The implementation of a derivative-free line search method further

supports the global convergence of the algorithm. Numerical experiments demonstrate that our proposed method

outperforms recent techniques in the literature, show- casing its efficiency and effectiveness.