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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Stoyanka G. Kostadinova & Stoil I. Ivanov, 2024. "Chebyshev’s Method for Multiple Zeros of Analytic Functions: Convergence, Dynamics and Real-World Applications," Mathematics, MDPI, vol. 12(19), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3043-:d:1488219
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