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 composition for nonlinear equation is performed, providing insights into both local and semilocal convergence properties. 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.