Convergence, Dynamics and Real-World Applications of C-H Method for Multiple Zeros of Analytic Functions
DOI:
https://doi.org/10.26713/cma.v17i1.3434Keywords:
Chebyshev method, Halley method, Multiple zeros, Analytic functions, Error estimates, Local convergence, Basins of attractionAbstract
In this study, we focus on the local convergence properties of the C-H combined mean technique applied to analytic functions having simple and multiple zeros. C-H combined mean technique is essentially the average of the two well-known approaches, the Halley’s method and the Chebyshev’s method. As an outcome, we provide a convergence theorem that guarantees the Q-cubic convergence of the C-H combined mean technique from the very beginning by giving precise domains of starting points together with error estimates. Furthermore, real-life applications demonstrate the robustness and efficiency of the C-H combined mean technique.
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