Homocentric convergence ball of the secant method

DOI10.1007/s11766-007-0313-3zbMath1150.65015OpenAlexW2103837007MaRDI QIDQ933062

Kewei Liang

Publication date: 6 August 2008

Published in: Applied Mathematics. Series B (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11766-007-0313-3

zbMATH Keywords

secant methodconvergence balllocal convergence theoremhomocentric ballsemi-local convergence theorem

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10)

Related Items

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 a Newton-Kurchatov-type method for non-differentiable operators, On the ball of convergence of secant-like methods for non-differentiable operators, Convergence of Steffensen's method for non-differentiable operators, Convergence analysis for single point Newton-type iterative schemes, How Many Steps Still Left to $x$*?

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence on a deformed Newton method
• Exact order of convergence of the secant method
• Local and global behavior for algorithms of solving equations
• On the error estimates of several Newton-like methods
• Finding zeros of analytic functions: \(\alpha\)-theory for secant type methods
• Mysovskii-type theorem for the Secant method under Hölder continuous Fréchet derivative
• On an iterative algorithm of order 1.839… for solving nonlinear operator equations^∗)
• Theory of Multivariate Secant Methods
• SOR-Secant Methods
• Convergence of Newton's method and uniqueness of the solution of equations in Banach space
• A Unified Convergence Theory for a Class of Iterative Processes