On Convergence of the Accelerated Newton Method Under Generalized Lipschitz Conditions

DOI10.1007/s10958-015-2645-5zbMath1349.47132OpenAlexW2279034333MaRDI QIDQ2808374

S. M. Shakhno

Publication date: 23 May 2016

Published in: Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-015-2645-5

zbMATH Keywords

convergencenonlinear functional equationaccelerated Newton method

Mathematics Subject Classification ID

Iteration theory, iterative and composite equations (39B12) Numerical solutions to equations with nonlinear operators (65J15) Nonlinear evolution equations (47J35)

Cites Work

• Newton-like methods for the computation of fixed points
• Steffensen method under generalized Lipschitz condition for the first-order divided differences.
• Über ein Verfahren der Ordnung \(1+\sqrt 2\) zur Nullstellenbestimmung
• Convergence behaviour of inexact Newton methods under weak Lipschitz condition.
• Convergence of inexact difference methods under the generalized Lipschitz conditions
• Convergence of Newton's method and uniqueness of the solution of equations in Banach space
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