From Halley to secant: redefining root finding with memory-based methods including convergence and stability

DOI10.1002/MMA.9876zbMATH Open1547.65051MaRDI QIDQ6559945

Amanullah Soomro, Ioannis K. Argyros, Sania Qureshi, Aydin Secer, Aisha A. Alshaery, Krzysztof Gdawiec, Amir Naseem

Publication date: 21 June 2024

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

Newton's methodzerosbasins of attractionefficiency indexlocal and semilocal analyses

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05) Rate of convergence, degree of approximation (41A25) Applications of functional analysis in numerical analysis (46N40)

Cites Work

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• Weaker conditions for the convergence of Newton's method
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• Machine-learning error models for approximate solutions to parameterized systems of nonlinear equations
• Some variants of Halley's method with memory and their applications for solving several chemical problems
• Some real-life applications of a newly constructed derivative free iterative scheme
• Computational geometry as a tool for studying root-finding methods
• The Theory and Applications of Iteration Methods
• Developing two efficient adaptive Newton‐type methods with memory
• ON INVERSE ITERATION PROCESS FOR FINDING ALL ROOTS OF NONLINEAR EQUATIONS WITH APPLICATIONS
• Semilocal convergence analysis of an efficient Steffensen-type fourth order method

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