CONVERGENCE ANALYSIS OF ITERATIVE COMPOSITIONS IN NONLINEAR MODELING: EXPLORING SEMILOCAL AND LOCAL CONVERGENCE PHENOMENA

In this work, a comprehensive analysis of a multi-step iterative com-position for nonlinear equations is performed, providing insights into both local and semilocal convergence properties. At each step three linear systems are solved in the method, but with the same linear operator. The analysis covers a wide range of applications, elucidating the parameters affecting both local and semilocal convergence and offering insightful information for optimizing iterative approaches in nonlinear model-solving tasks. Moreover, we assert the solution’s uniqueness by supplying the necessary standards inside the designated field. Lastly, we apply our theoretical deductions to real-world problems and show the related test results to validate our findings.