A sixth order transformation method for finding multiple roots of nonlinear equations and basin attractors for various methods

Sharma, Rajni; Bahl, Ashu

doi:10.1016/j.amc.2015.07.056

Cited by 3 publications

(3 citation statements)

References 32 publications

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“…A new fifth-order modified Newton's method for finding multiple roots of nonlinear equations with unknown multiplicity was developed by Li et al [19]. Sharma and Bahl [20] proposed a sixth-order modified Newton's method based on Traub's [16] transformation. Jaiswal [21] claimed to be the first to propose an optimal eighth-order method for multiple roots of unknown multiplicity.…”

Section: Introductionmentioning

confidence: 99%

Modification of Newton-Househölder Method for Determining Multiple Roots of Unknown Multiplicity of Nonlinear Equations

et al. 2021

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In this study, we propose an extension of the modified Newton-Househölder methods to find multiple roots with unknown multiplicity of nonlinear equations. With four functional evaluations per iteration, the proposed method achieves an optimal eighth order of convergence. The higher the convergence order, the quicker we get to the root with a high accuracy. The numerical examples have shown that this scheme can compete with the existing methods. This scheme is also stable across all of the functions tested based on the graphical basins of attraction.

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Section: Introductionmentioning

confidence: 99%

Modification of Newton-Househölder Method for Determining Multiple Roots of Unknown Multiplicity of Nonlinear Equations

et al. 2021

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“…In this portion, we employ the proposed three-step method Equation (15) (MM8) for solving five nonlinear equations and scrutinize them by the methods given by Sharma and Bahl Equation (9) (MM6), in [24], and the Li et al Equation (8) (MM5), in [23]. Displayed in Tables 1-3 are the absolute error in the root, the absolute value of the function and the absolute error in the approximation of unknown multiplicity, for three iterations.…”

Section: Numerical Testing With the Conclusionmentioning

confidence: 99%

“…More recently, by using the same transformation, Sharma and Bahl [24] proposed an iterative scheme with a convergence rate of six and expressed as:…”

Section: Introductionmentioning

confidence: 99%

An Optimal Order Method for Multiple Roots in Case of Unknown Multiplicity

Jaiswal

2016

Algorithms

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Abstract:In the literature, recently, some three-step schemes involving four function evaluations for the solution of multiple roots of nonlinear equations, whose multiplicity is not known in advance, are considered, but they do not agree with Kung-Traub's conjecture. The present article is devoted to the study of an iterative scheme for approximating multiple roots with a convergence rate of eight, when the multiplicity is hidden, which agrees with Kung-Traub's conjecture. The theoretical study of the convergence rate is investigated and demonstrated. A few nonlinear problems are presented to justify the theoretical study.

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Convergence of iterative methods for multiple zeros

Magreñán¹,

Argyros²

2018

A Contemporary Study of Iterative Methods

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A sixth order transformation method for finding multiple roots of nonlinear equations and basin attractors for various methods

Cited by 3 publications

References 32 publications

Modification of Newton-Househölder Method for Determining Multiple Roots of Unknown Multiplicity of Nonlinear Equations

Modification of Newton-Househölder Method for Determining Multiple Roots of Unknown Multiplicity of Nonlinear Equations

An Optimal Order Method for Multiple Roots in Case of Unknown Multiplicity

Convergence of iterative methods for multiple zeros

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