A Novel n-Point Newton-Type Root-Finding Method of High Computational Efficiency

A novel Newton-type n-point iterative method with memory is proposed for solving nonlinear equations, which is constructed by the Hermite interpolation. The proposed iterative method with memory reaches the order (2n+2n−1−1+22n+1+22n−2+2n+1)/2 by using n variable parameters. The computational effici...

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Bibliographic Details
Published inMathematics (Basel) Vol. 10; no. 7; p. 1144
Main Author Wang, Xiaofeng
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.04.2022
Subjects
Approximation
Attraction
Basins
Computational efficiency
Computing time
Efficiency
Interpolation
Iterative methods
Mathematics
Methods
nonlinear equation
Nonlinear equations
Numerical methods
optimal convergence order
Stability
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Summary:A novel Newton-type n-point iterative method with memory is proposed for solving nonlinear equations, which is constructed by the Hermite interpolation. The proposed iterative method with memory reaches the order (2n+2n−1−1+22n+1+22n−2+2n+1)/2 by using n variable parameters. The computational efficiency of the proposed method is higher than that of the existing Newton-type methods with and without memory. To observe the stability of the proposed method, some complex functions are considered under basins of attraction. Basins of attraction show that the proposed method has better stability and requires a lesser number of iterations than various well-known methods. The numerical results support the theoretical results.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math10071144