The secant method for nondifferentiable operators

DOI10.1016/S0893-9659(01)00150-1zbMath1016.65033OpenAlexW2036827279MaRDI QIDQ1861778

M. J. Rubio, Miguel A. Hernández

Publication date: 10 March 2003

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0893-9659(01)00150-1

zbMATH Keywords

semilocal convergenceBanach spacenonlinear operatornondifferentiable operatorsecant methoddivided difference operator

Mathematics Subject Classification ID

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

Related Items (30)

Improving the applicability of the secant method to solve nonlinear systems of equations ⋮ New sufficient convergence conditions of the secant method for nondifferentiable operators ⋮ A new semilocal convergence theorem for the secant method under Hölder continuous divided differences ⋮ Extended two-step-Kurchatov method for solving Banach space valued nondifferentiable equations ⋮ Convergence of the two-step combined method and uniqueness of the solution of nonlinear operator equations ⋮ An improvement of the Kurchatov method by means of a parametric modification ⋮ Chebyshev-secant-type methods for non-differentiable operators ⋮ Kurchatov-type methods for non-differentiable Hammerstein-type integral equations ⋮ A family of derivative-free methods for nonlinear equations ⋮ A modification of Newton's method for nondifferentiable equations. ⋮ An uniparametric secant-type method for nonsmooth generalized equations ⋮ A Steffensen type method of two steps in Banach spaces with applications ⋮ Extending the convergence domain of the secant and Moser method in Banach space ⋮ Convergence analysis of a family of Steffensen-type methods for generalized equations ⋮ Extended semilocal convergence for the Newton-Kurchatov method ⋮ A Traub type result for one-point iterative methods with memory ⋮ Two-step solver for equations with nondifferentiable term ⋮ Mysovskii-type theorem for the Secant method under Hölder continuous Fréchet derivative ⋮ Secant method with regularly continuous divided differences ⋮ A new semilocal convergence theorem for a fast iterative method with nondifferentiable operators ⋮ The convergence ball of the secant method under Hölder continuous divided differences ⋮ On semilocal convergence of three-step Kurchatov method under weak condition ⋮ Three step Kurchatov method for nondifferentiable operators ⋮ On an improved local convergence analysis for the Secant method ⋮ On a Newton-Kurchatov-type Iterative Process ⋮ Achieving an extended convergence analysis for the secant method under a restricted Hölder continuity condition ⋮ Ulm's method without derivatives ⋮ Convergence analysis for the secant method based on new recurrence relations ⋮ Local and semilocal convergence for Kurchatov method under \(\omega\)-continuity conditions ⋮ Extended convergence analysis of the Newton–Potra method under weak conditions

Cites Work

• The secant method and fixed points of nonlinear operators
• Regula-falsi-Verfahren mit konsistenter Steigung und Majorantenprinzip
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