On an iterative algorithm with superquadratic convergence for solving nonlinear operator equations

DOI10.1016/j.cam.2009.02.010zbMath1225.65062OpenAlexW1975620936MaRDI QIDQ2389554

S. M. Shakhno

Publication date: 17 July 2009

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

Full work available at URL: https://doi.org/10.1016/j.cam.2009.02.010

zbMATH Keywords

algorithmsBanach spaceserror estimatesnumerical examplesnonlinear boundary value problemsystems of nonlinear equationsnonlinear operator equationsdivided differencesconvergence orderMajorant methoditerative difference methodLipschitz-Hölder condition

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Iterative procedures involving nonlinear operators (47J25) Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solutions to equations with nonlinear operators (65J15) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (9)

Convergence of the two-step combined method and uniqueness of the solution of nonlinear operator equations ⋮ Local and semi-local convergence for Chebyshev two point like methods with applications in different fields ⋮ Newton-Type Solvers Using Outer Inverses for Singular Equations ⋮ Frozen iterative methods using divided differences ``à la Schmidt-Schwetlick ⋮ Two-step solver for equations with nondifferentiable term ⋮ Two-step solver for nonlinear equations ⋮ CONSTRUCTION OF DERIVATIVE-FREE ITERATIVE METHODS FROM CHEBYSHEV'S METHOD ⋮ Local convergence comparison between frozen Kurchatov and Schmidt-Schwetlick-Kurchatov solvers with applications ⋮ On Convergence and Efficiency in the Resolution of Systems of Nonlinear Equations from a Local Analysis

Cites Work

• Über ein Verfahren der Ordnung \(1+\sqrt 2\) zur Nullstellenbestimmung
• Some supplementary results on the \(1+\sqrt 2\) order method for the solution of nonlinear equations
• On an iterative algorithm for solving nonlinear operator equations
• Inexact trust region method for large sparse systems of nonlinear equations
• Application of nonlinear majorants for investigation of the secant method for solving nonlinear equations.
• The secant method and divided differences Hölder continuous
• On a Kurchatov's method of linear interpolation for solving nonlinear equations
• On an iterative algorithm of order 1.839… for solving nonlinear operator equations^∗)
• A New Sparsity Preserving Quasi-Newton Update for Solving Nonlinear Equations
• Eine Übertragung der Regula Falsi auf Gleichungen in Banachräumen I
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