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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Vydáno v:	International journal of computer mathematics Ročník 98; číslo 5; s. 1049 - 1068
Hlavní autoři:	Usurelu, Gabriela Ioana, Bejenaru, Andreea, Postolache, Mihai
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Abingdon Taylor & Francis 04.05.2021 Taylor & Francis Ltd
Témata:	Iterative process Newton methods Newton's method Polynomials polynomiography root-finding algorithm simulation Stability analysis
ISSN:	0020-7160, 1029-0265
On-line přístup:	Získat plný text
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Popis
Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0020-7160 1029-0265
DOI:	10.1080/00207160.2020.1802017