A Kantorovich-type analysis for a fast iterative method for solving nonlinear equations

DOI10.1016/j.jmaa.2006.09.075zbMath1121.65061OpenAlexW1965459507MaRDI QIDQ881993

Ioannis K. Argyros

Publication date: 23 May 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.09.075

zbMATH Keywords

numerical examplesquadratic convergenceBanach spacesecant methodLipschitz conditionnonlinear operator equationsradius of convergencedivided differencesmajorant principlelocal/semilocal convergence

Mathematics Subject Classification ID

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

Related Items (17)

A non-iterative derivative-free method for nonlinear ordinary differential equations ⋮ On the efficiency of two variants of Kurchatov's method for solving nonlinear systems ⋮ Extended two-step-Kurchatov method for solving Banach space valued nondifferentiable equations ⋮ Unified majorizing sequences for Traub-type multipoint iterative procedures ⋮ Local convergence of a secant type method for solving least squares problems ⋮ A multidimensional generalization of some classes of free-derivative iterative methods to solve nonlinear equations ⋮ On the convergence of Kurchatov-type methods using recurrent functions for solving equations ⋮ A derivative free iterative method for solving least squares problems ⋮ On a quadratically convergent method using divided differences of order one under the gamma condition ⋮ A Fréchet derivative-free cubically convergent method for set-valued maps ⋮ On the Kurchatov method for solving equations under weak conditions ⋮ Frozen iterative methods using divided differences ``à la Schmidt-Schwetlick ⋮ Semilocal convergence of secant-like methods for differentiable and nondifferentiable operator equations ⋮ A new semilocal convergence theorem for a fast iterative method with nondifferentiable operators ⋮ Local convergence comparison between frozen Kurchatov and Schmidt-Schwetlick-Kurchatov solvers with applications ⋮ Convergence criterion and convergence ball of the Newton-type method in Banach space ⋮ Extended local and semilocal convergence for interpolatory iterative methods for nonlinear equations

Uses Software

• BRENT

Cites Work

• On a higher order secant method.
• A modified secant method for semismooth equations
• A class of quasi-Newton generalized Steffensen methods on Banach spaces
• A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
• Semilocal convergence of the secant method under mild convergence conditions of differentiability
• Secant-like methods for solving nonlinear integral equations of the Hammerstein type
• On an iterative algorithm of order 1.839… for solving nonlinear operator equations^∗)
• On the convergence of a class of generalized steffensen's iterative procedures and error analysis
• Multipoint Super-Halley Type Approximation Algorithms in Banach Spaces
• On a two-point Newton-like method of convergent order two
• On the local convergence of secant-type methods
• A new high order method of regula falsi type for computing a root of an equation
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