A semilocal convergence result for Newton's method under generalized conditions of Kantorovich

DOI10.1016/j.jco.2013.12.006zbMath1286.65068OpenAlexW2014383712MaRDI QIDQ2442863

D. González, José Antonio Ezquerro, Miguel Ángel Hernández-Verón

Publication date: 1 April 2014

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2013.12.006

zbMATH Keywords

Newton's methodnumerical examplessemilocal convergencenonlinear operator equationa priori error estimatesNewton-Kantorovich theoremmajorizing sequenceconservative problem

Mathematics Subject Classification ID

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

Related Items (6)

The convergence ball and error analysis of the two-step secant method ⋮ On the existence of solutions of nonlinear Fredholm integral equations from Kantorovich's technique ⋮ Semilocal Convergence Theorem for a Newton-like Method ⋮ Semilocal convergence analysis of \(S\)-iteration process of Newton-Kantorovich like in Banach spaces ⋮ On the convergence of inexact Newton-like methods under mild differentiability conditions ⋮ The convergence ball and error analysis of the relaxed secant method

Cites Work

• A new semilocal convergence theorem for Newton's method
• Majorizing sequences for Newton's method from initial value problems
• Halley's method for operators with unbounded second derivative
• A family of Halley-Chebyshev iterative schemes for non-Fréchet differentiable operators
• A convergence theorem for Newton-like methods in Banach spaces
• On the convergence of Newton's method for polynomial equations and applications in radiative transfer
• On the Newton-Kantorovich hypothesis for solving equations
• A modification of the classic conditions of Newton-Kantorovich for Newton's method
• Third-order iterative methods under Kantorovich conditions
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