Improving the domain of parameters for Newton's method with applications

DOI10.1016/J.CAM.2016.11.019zbMath1357.65066OpenAlexW2550290838MaRDI QIDQ507862

Ioannis K. Argyros, Juan Antonio Sicilia, Ángel Alberto Magreñán

Publication date: 9 February 2017

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2016.11.019

zbMATH Keywords

numerical exampleNewton's methoderror boundBanach spacedomain of parametersmajorizing sequencelocal/semilocal convergencenonlinear operator euqations

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Cites Work

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• Different anomalies in a Jarratt family of iterative root-finding methods
• On an improved convergence analysis of Newton's method
• A new tool to study real dynamics: the convergence plane
• Weaker conditions for the convergence of Newton's method
• The application of Newton's method in vector form for solving nonlinear scalar equations where the classical Newton method fails
• How to improve the domain of parameters for Newton's method
• On the local convergence and the dynamics of Chebyshev-Halley methods with six and eight order of convergence
• On the local convergence of fast two-step Newton-like methods for solving nonlinear equations
• Chaotic dynamics of a third-order Newton-type method
• Convergence and Applications of Newton-type Iterations

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