New Optimal Newton-Householder Methods for Solving Nonlinear Equations and their Dynamics

Sariman, Syahmi Afandi; Hashim, Ishak

doi:10.32604/cmc.2020.010836

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Development Of the Methods And Convergence Analysis2

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2023

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Cited by 11 publications

(2 citation statements)

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“…By eliminating the second derivative, the Househölder method can be made optimal. A modified version of the three-step Newton-Househölder method for approximating a simple root has been proposed by Sariman and Hashim [24] recently. The method is optimal and of eight order.…”

Section: Development Of the Methods And Convergence Analysismentioning

confidence: 99%

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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: Development Of the Methods And Convergence Analysismentioning

confidence: 99%

“…Similarly, the parameter values in (24), and α = 10 and β = 4 yield a scheme with the first two steps exactly the same as in ( 26) and a slightly different last step as follows:…”

Section: Development Of the Methods And Convergence Analysismentioning

confidence: 99%