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Mathematics
Volume 12
Issue 19
10.3390/math12193043
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

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

by
Stoyanka G. Kostadinova
and
Stoil I. Ivanov
*
Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(19), 3043; https://doi.org/10.3390/math12193043 (registering DOI)
Submission received: 8 September 2024 / Revised: 24 September 2024 / Accepted: 26 September 2024 / Published: 28 September 2024
(This article belongs to the Special Issue Computational Mathematics and Numerical Analysis)
Versions Notes

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 iteration methods; Chebyshev’s method; analytic functions; multiple zeros; local convergence; error estimates; basins of attraction

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MDPI and ACS Style

Kostadinova, S.G.; Ivanov, S.I. Chebyshev’s Method for Multiple Zeros of Analytic Functions: Convergence, Dynamics and Real-World Applications. Mathematics 2024, 12, 3043. https://doi.org/10.3390/math12193043

AMA Style

Kostadinova SG, Ivanov SI. Chebyshev’s Method for Multiple Zeros of Analytic Functions: Convergence, Dynamics and Real-World Applications. Mathematics. 2024; 12(19):3043. https://doi.org/10.3390/math12193043

Chicago/Turabian Style

Kostadinova, Stoyanka G., and Stoil I. Ivanov. 2024. "Chebyshev’s Method for Multiple Zeros of Analytic Functions: Convergence, Dynamics and Real-World Applications" Mathematics 12, no. 19: 3043. https://doi.org/10.3390/math12193043

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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