Newton-like methods and polynomiographic visualization of modified Thakur processes

The content of this paper is twofold. First, it aims to provide some new Newton-like methods for solving the root-finding problem in the complex plane. Moreover a convergence test for the resulted methods is phrased and proved. The pseudo-Newton method of Kalantari for finding the maximum modulus of...

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Bibliographic Details
Published inInternational journal of computer mathematics Vol. 98; no. 5; pp. 1049 - 1068
Main Authors Usurelu, Gabriela Ioana, Bejenaru, Andreea, Postolache, Mihai
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.05.2021
Taylor & Francis Ltd
Subjects
Iterative process
Newton methods
Newton's method
Polynomials
polynomiography
root-finding algorithm
simulation
Stability analysis
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ISSN0020-7160
1029-0265
DOI10.1080/00207160.2020.1802017

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Summary:The content of this paper is twofold. First, it aims to provide some new Newton-like methods for solving the root-finding problem in the complex plane. Moreover a convergence test for the resulted methods is phrased and proved. The pseudo-Newton method of Kalantari for finding the maximum modulus of complex polynomials arises as particular case of the newly proposed procedures. Secondly, a recently introduced Thakur iterative process is used in connection with the newly described methods. Its stability and data dependence is subject to analysis. Ultimately, an illustrative analysis regarding some modified Thakur iteration procedures, is obtained via polynomiographic techniques.
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ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2020.1802017