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

Stoyanka G. Kostadinova and Stoil I. Ivanov ()
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Stoyanka G. Kostadinova: Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
Stoil I. Ivanov: Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria

Mathematics, 2024, vol. 12, issue 19, 1-15

Abstract: 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.

Keywords: iteration methods; Chebyshev’s method; analytic functions; multiple zeros; local convergence; error estimates; basins of attraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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