Avoiding the computation of the second Fréchet-derivative in the convex acceleration of Newton's method

DOI10.1016/S0377-0427(98)00083-1zbMath0945.65060OpenAlexW1972187745MaRDI QIDQ1298644

José Antonio Ezquerro, Miguel A. Hernández

Publication date: 21 September 2000

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

Full work available at URL: https://doi.org/10.1016/s0377-0427(98)00083-1

zbMATH Keywords

numerical examplesBanach spacenonlinear operator equationthird-order convergencetwo-point iteration

Mathematics Subject Classification ID

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

Related Items (19)

On a two-step Kurchatov-type method in Banach space ⋮ Semilocal convergence of a family of third-order methods in Banach spaces under Hölder continuous second derivative ⋮ Convergence of the variants of the Chebyshev-Halley iteration family under the Hölder condition of the first derivative ⋮ Fourth-order iterative methods free from second derivative ⋮ Recurrence relations for semilocal convergence of a fifth-order method in Banach spaces ⋮ A new class of root-finding methods in \({\mathbb {R}}^n\): the inexact tensor-free Chebyshev-Halley class ⋮ Recurrence relations for semilocal convergence of a Newton-like method in Banach spaces ⋮ New iterative technique for solving a system of nonlinear equations ⋮ Constructing third-order derivative-free iterative methods ⋮ Some variants of Cauchy's method with accelerated fourth-order convergence ⋮ ON THE R-ORDER CONVERGENCE OF A THIRD ORDER METHOD IN BANACH SPACES UNDER MILD DIFFERENTIABILITY CONDITIONS ⋮ A Stirling-like method with Hölder continuous first derivative in Banach spaces ⋮ Convergence of the family of the deformed Euler--Halley iterations under the Hölder condition of the second derivative ⋮ Convergence of a continuation method under the Hölder condition of the first derivative ⋮ Local convergence of super Halley's method under weaker conditions on Fréchet derivative in Banach spaces ⋮ Deformed super-Halley's iteration in Banach spaces and its local and semilocal convergence ⋮ Unified convergence for multi-point super Halley-type methods with parameters in Banach space ⋮ Historical developments in convergence analysis for Newton's and Newton-like methods ⋮ Semilocal convergence for Super-Halley's method under \(\omega\)-differentiability condition

Cites Work

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• Recurrence relations for rational cubic methods. I: The Halley method
• On the method of tangent hyperbolas in Banach spaces
• The Jarratt method in Banach space setting
• A local convergence theorem for the super-Halley method in a Banach space
• Quadratic equations in Banach spaces
• A family of chebyshev-halley type methods
• A family of Chebyshev-Halley type methods in Banach spaces
• Some iteration methods of solving non-linear equations with non-differentiable operators

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