Recurrence relations for semilocal convergence of a Newton-like method in Banach spaces

DOI10.1016/j.jmaa.2008.03.064zbMath1160.65024OpenAlexW1969442324MaRDI QIDQ931004

Elsie Sterbin Gottlieb

Publication date: 24 June 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.03.064

zbMATH Keywords

Banach spacesnumerical examplesrecurrence relationscubic convergenceLipschitz continuousHölder continuity conditionmultipoint third order Newton-like methodssecond Fréchet derivative

Mathematics Subject Classification ID

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

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Cites Work

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• Recurrence relations for rational cubic methods. II: The Chebyshev method
• Recurrence relations for rational cubic methods. I: The Halley method
• Recurrence relations for the super-Halley method
• Reduced recurrence relations for the Chebyshev method
• Avoiding the computation of the second Fréchet-derivative in the convex acceleration of Newton's method
• Second-derivative-free variant of the Chebyshev method for nonlinear equations
• On the \(R\)-order of the Halley method
• Recurrence relations for a Newton-like method in Banach spaces
• Third-order convergence theorem by using majorizing function for a modified Newton method in Banach space
• Convergence of the family of the deformed Euler--Halley iterations under the Hölder condition of the second derivative
• Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method
• Chebyshev's approximation algorithms and applications

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