On an improved local convergence analysis for the Secant method

DOI10.1007/s11075-009-9271-6zbMath1176.65068OpenAlexW2083300135MaRDI QIDQ735074

Ioannis K. Argyros, Hongmin Ren

Publication date: 14 October 2009

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-009-9271-6

zbMATH Keywords

numerical exampleBanach spacesNewton's methodnonlinear operator equationlocal convergencesecant methodFréchet-derivativeradius of convergence

Mathematics Subject Classification ID

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

Related Items (13)

Improving the accessibility of Steffensen's method by decomposition of operators ⋮ A significant improvement of a family of secant-type methods ⋮ Dynamics and local convergence of a family of derivative-free iterative processes ⋮ On the Convergence of Secant-Like Methods ⋮ On the local convergence of Kung-Traub's two-point method and its dynamics. ⋮ On the local convergence of a Newton-Kurchatov-type method for non-differentiable operators ⋮ On the ball of convergence of secant-like methods for non-differentiable operators ⋮ A study on the local convergence and dynamics of the two-step and derivative-free Kung-Traub's method ⋮ Convergence of Steffensen's method for non-differentiable operators ⋮ Unnamed Item ⋮ Convergence analysis for single point Newton-type iterative schemes ⋮ Two-point methods for solving equations and systems of equations ⋮ Achieving an extended convergence analysis for the secant method under a restricted Hölder continuity condition

Cites Work

• A new semilocal convergence theorem for the secant method under Hölder continuous divided differences
• The secant method and fixed points of nonlinear operators
• Regula-falsi-Verfahren mit konsistenter Steigung und Majorantenprinzip
• The convergence ball of Newton's method and the uniqueness ball of equations under Hölder-type continuous derivatives
• The secant method and divided differences Hölder continuous
• The secant method for nondifferentiable operators
• 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
• Mysovskii-type theorem for the Secant method under Hölder continuous Fréchet derivative
• The convergence ball of the secant method under Hölder continuous divided differences
• Convergence and Applications of Newton-type Iterations
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