A modification of the classical Kantorovich conditions for Newton's method

DOI10.1016/S0377-0427(01)00393-4zbMath0992.65057MaRDI QIDQ5953960

Miguel A. Hernández

Publication date: 1 September 2002

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

zbMATH Keywords

Newton's methodBanach spaceFréchet derivativenonlinear operator equationsKantorovich condition

Mathematics Subject Classification ID

Numerical solutions to equations with nonlinear operators (65J15)

Related Items (13)

Weak convergence conditions for the Newton's method in Banach space using general majorizing sequences ⋮ Expanding the applicability of Newton's method using Smale's \(\alpha\)-theory ⋮ Estimating upper bounds on the limit points of majorizing sequences for Newton's method ⋮ Extended Kantorovich theory for solving nonlinear equations with applications ⋮ Weaker conditions for the convergence of Newton's method ⋮ The majorant method in the theory of Newton-Kantorovich approximations and generalized Lipschitz conditions ⋮ On the semilocal convergence of the Halley method using recurrent functions ⋮ Third-order convergence theorem by using majorizing function for a modified Newton method in Banach space ⋮ New conditions for the convergence of Newton-like methods and applications ⋮ On the midpoint method for solving equations ⋮ Convergence analysis for a deformed Newton's method with third-order in Banach space under γ-condition ⋮ Extending the applicability of Newton’s method using nondiscrete induction ⋮ Expanding the applicability of Newton’s method and of a robust modified Newton’s method

Cites Work

• A new semilocal convergence theorem for Newton's method
• The Newton-Kantorovich method under mild differentiability conditions and the Ptâk error estimates
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