New sufficient convergence conditions of the secant method for nondifferentiable operators

DOI10.1016/j.amc.2006.05.009zbMath1111.65050OpenAlexW2059500334MaRDI QIDQ858786

Hongmin Ren

Publication date: 11 January 2007

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.05.009

zbMATH Keywords

numerical examplesemilocal convergenceBanach spacenonlinear operator equationdivided differences

Mathematics Subject Classification ID

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

Related Items (8)

Extended two-step-Kurchatov method for solving Banach space valued nondifferentiable equations ⋮ Majorizing sequences for iterative procedures in Banach spaces ⋮ On a quadratically convergent method using divided differences of order one under the gamma condition ⋮ A new semilocal convergence theorem for a fast iterative method with nondifferentiable operators ⋮ On semilocal convergence of three-step Kurchatov method under weak condition ⋮ Three step Kurchatov method for nondifferentiable operators ⋮ Local and semilocal convergence for Kurchatov method under \(\omega\)-continuity conditions ⋮ Extended convergence analysis of the Newton–Potra method under weak conditions

Cites Work

• Unnamed Item
• Regula-falsi-Verfahren mit konsistenter Steigung und Majorantenprinzip
• The secant method for nondifferentiable operators
• Semilocal convergence of the secant method under mild convergence conditions of differentiability
• On the secant method for solving nonsmooth equations

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