Mean Iterative Approach for Multiple Polynomial Zeros and Convergence - Das, Rajat Subhra; Kumar, Abhimanyu (Communications in Mathematics and Applications, 2025)
In this study, we propose a mean iterative approach of third order for solving a polynomial equation that has multiple type zeros. We used three prominent third-order algorithms for this build: Chebyshev, Halley and Super-Halley (CHS). For this CHS Combined Mean Method, we developed two forms of local convergence theorems to determine the convergence. We used the gauge function to determine the convergence of our technique. We employed two distinct forms of initial conditions on a field with norm to prove the local convergence theorems for the CHS combined mean technique. Our convergence analysis includes error estimates.