Newton-like methods for the computation of fixed points

DOI10.1016/0898-1221(84)90088-9zbMath0538.65035OpenAlexW2008560605MaRDI QIDQ793499

Wilhelm Werner

Publication date: 1984

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(84)90088-9

zbMATH Keywords

convergencefixed pointsnumerical exampleerror estimatesNewton's methodcontractionBanach spaceoptimal parameterStirling method

Mathematics Subject Classification ID

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

Related Items (29)

A third order method for fixed points in Banach spaces ⋮ A modified Chebyshev's iterative method with at least sixth order of convergence ⋮ A two-step Steffensen's method under modified convergence conditions ⋮ Third-order iterative methods under Kantorovich conditions ⋮ Solving the one dimensional Bratu problem with efficient fourth order iterative methods ⋮ Expanding the applicability of Stirling's method under weaker conditions and restricted convergence regions ⋮ On the Convergence of Secant-Like Methods ⋮ Geometric constructions of iterative functions to solve nonlinear equations ⋮ Semilocal convergence of a sixth order iterative method for quadratic equations ⋮ Third-order iterative methods without using any Fréchet derivative. ⋮ A fast Chebyshev's method for quadratic equations. ⋮ A Newton-like method for generalized operator equations in Banach spaces ⋮ Secant-like methods for solving nonlinear integral equations of the Hammerstein type ⋮ A new iterative method of asymptotic order 1+√2 for the computation of fixed points ⋮ Some variants of Cauchy's method with accelerated fourth-order convergence ⋮ Convergence by nondiscrete mathematical induction of a two step secant's method ⋮ A Traub type result for one-point iterative methods with memory ⋮ Convergence and numerical analysis of a family of two-step Steffensen's methods ⋮ An adaptive version of a fourth-order iterative method for quadratic equations ⋮ A Stirling-like method with Hölder continuous first derivative in Banach spaces ⋮ Semilocal convergence of Stirling's method under Hölder continuous first derivative in Banach spaces ⋮ On the convergence of inexact two-step Newton-like algorithms using recurrent functions ⋮ Convergence of Stirling's method under weak differentiability condition ⋮ On Convergence of the Accelerated Newton Method Under Generalized Lipschitz Conditions ⋮ The application of an inverse-free Jarratt-type approximation to nonlinear integral equations of Hammerstein-type ⋮ A family of Halley-Chebyshev iterative schemes for non-Fréchet differentiable operators ⋮ SEMILOCAL CONVERGENCE OF A STIRLING-LIKE METHOD IN BANACH SPACES ⋮ Relaxing convergence conditions for Stirling's method ⋮ Accessibility of solutions of operator equations by Newton-like methods

Cites Work

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• Über ein Verfahren der Ordnung \(1+\sqrt 2\) zur Nullstellenbestimmung
• Some supplementary results on the \(1+\sqrt 2\) order method for the solution of nonlinear equations
• Convergence of Stirling's method in Banach spaces
• Newton's Method in Banach Spaces
• The Convergence of Single-Rank Quasi-Newton Methods

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