Memory Based Approaches to One-Dimensional Nonlinear Models

Algorithms that locate roots are used to analyze nonlinear equations in computer science, mathematics, and physical sciences. In order to speed up convergence and increase computational efficiency, memory-based root-seeking algorithms may look for the previous iterations. Three memory-based methods...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2025-02, Vol.195 (1), p.1, Article 1
Main Authors: Naseem, Amir, Argyros, Ioannis K., Qureshi, Sania, Aziz ur Rehman, Muhammad, Soomro, Amanullah, Gdawiec, Krzysztof, Iyanda Abdulganiy, Ridwanulahi
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Approximation
Calculus of Variations and Optimal Control
Optimization
Computational Mathematics and Numerical Analysis
Computer engineering
Convergence
Dimensional analysis
Efficiency
Finite differences
Iterative methods
Mathematics
Mathematics and Statistics
Methods
Nonlinear equations
Operators (mathematics)
Partial Differential Equations
Physical sciences
Probability Theory and Stochastic Processes
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Summary:Algorithms that locate roots are used to analyze nonlinear equations in computer science, mathematics, and physical sciences. In order to speed up convergence and increase computational efficiency, memory-based root-seeking algorithms may look for the previous iterations. Three memory-based methods with a convergence order of about 2.4142 and one method without memory with third-order convergence are devised using both Taylor’s expansion and the backward difference operator. We provide an extensive analysis of local and semilocal convergence. We also use polynomiography to analyze the methods visually. Finally, the proposed iterative approaches outperform a number of existing memory-based methods when applied to one-dimensional nonlinear models taken from different fields of science and engineering.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-024-00703-9