Chebyshev’s Method for Multiple Zeros of Analytic Functions: Convergence, Dynamics and Real-World Applications

This paper deals with the convergence and dynamics of Chebyshev’s method for simple and multiple zeros of analytic functions. We establish a local convergence theorem that provides error estimates and exact domains of initial approximations to guarantee the Q-cubic convergence of the method right from the first iteration. Applications to some real-world problems as well as theoretical and numerical comparison with the famous Halley’s method are also provided.