Local convergence analysis of an eighth order scheme using hypothesis only on the first derivative

DOI10.3390/a9040065zbMath1461.65098OpenAlexW2525583675MaRDI QIDQ1736834

Xianqiang Yang

Publication date: 26 March 2019

Published in: Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3390/a9040065

zbMATH Keywords

Banach spacelocal convergenceLipschitz constantradius of convergencedivided differenceKung-Traub method

Mathematics Subject Classification ID

Numerical solutions to equations with nonlinear operators (65J15)

Related Items (1)

Local Convergence of a Family of Iterative Methods with Sixth and Seventh Order Convergence Under Weak Conditions

Cites Work

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• Different anomalies in a Jarratt family of iterative root-finding methods
• A new tool to study real dynamics: the convergence plane
• Basin attractors for various methods
• Basins of attraction for several methods to find simple roots of nonlinear equations
• Dynamics of the King and Jarratt iterations
• On the local convergence of fast two-step Newton-like methods for solving nonlinear equations
• Chaotic dynamics of a third-order Newton-type method
• An efficient family of weighted-Newton methods with optimal eighth order convergence
• A modified Chebyshev's iterative method with at least sixth order of convergence
• New iterations of \(R\)-order four with reduced computational cost
• Simply constructed family of a Ostrowski's method with optimal order of convergence
• Convergence and Applications of Newton-type Iterations
• A variant of Newton's method with accelerated third-order convergence

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