On the local convergence of secant-type methods

DOI10.1080/00207160412331284123zbMath1068.65068OpenAlexW2076492844MaRDI QIDQ4823353

Sergio Amat, Sonia Busquier, José Manuel Gutiérrez Jimenez

Publication date: 27 October 2004

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160412331284123

zbMATH Keywords

numerical examplesBanach spaceNewton methodnonlinear operator equationlocal convergenceradius of convergencesecant methods

Mathematics Subject Classification ID

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

Related Items (19)

Secant-like methods for solving nonlinear models with applications to chemistry ⋮ Optimizing the applicability of a theorem by F. Potra for Newton-like methods ⋮ Convergence analysis of the secant type methods ⋮ A two-step Steffensen's method under modified convergence conditions ⋮ New semilocal and local convergence analysis for the secant method ⋮ Extended two-step-Kurchatov method for solving Banach space valued nondifferentiable equations ⋮ A Kantorovich-type analysis for a fast iterative method for solving nonlinear equations ⋮ Computing multiple zeros by using a parameter in Newton-secant method ⋮ A semilocal convergence for a uniparametric family of efficient secant-like methods ⋮ On a quadratically convergent method using divided differences of order one under the gamma condition ⋮ New improved convergence analysis for the secant method ⋮ On the local convergence of a Newton-Kurchatov-type method for non-differentiable operators ⋮ Expanding the applicability of a third order Newton-type method free of bilinear operators ⋮ A Steffensen's type method in Banach spaces with applications on boundary-value problems ⋮ Majorizing sequences for Newton's method under centred conditions for the derivative ⋮ On the local convergence of a deformed Newton's method under Argyros-type condition ⋮ Influence of the center condition on the two-step secant method ⋮ On a third-order Newton-type method free of bilinear operators ⋮ Unnamed Item

Cites Work

• On Q-order and R-order of convergence
• Secant methods for semismooth equations
• On a higher order secant method.
• A modified secant method for semismooth equations
• Local Convergence of Inexact Newton Methods
• A Mesh-Independence Principle for Operator Equations and Their Discretizations
• A Local Convergence Theory for Combined Inexact-Newton/Finite-Difference Projection Methods

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