Newton-like methods under mild differentiability conditions with error analysis

DOI10.1017/S0004972700004238zbMath0629.65061OpenAlexW2047235050MaRDI QIDQ3766727

Ioannis K. Argyros

Publication date: 1988

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972700004238

zbMATH Keywords

convergenceBanach spaceserror analysisNewton-like methods

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Extrapolation to the limit, deferred corrections (65B05) Numerical solutions to equations with nonlinear operators (65J15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (19)

Solving symmetric algebraic Riccati equations with high order iterative schemes ⋮ A NEWTON-LIKE METHOD FOR SOLVING SOME BOUNDARY VALUE PROBLEMS ⋮ Application of iterative processes of \(R\)-order at least three to operators with unbounded second derivative ⋮ Improved error bounds for the modified secant method ⋮ On the Convergence of Secant-Like Methods ⋮ An Ulm-type method with \(R\)-order of convergence three ⋮ Error for the modified secant method ⋮ A variant of the Newton-Kantorovich theorem for nonlinear integral equations of mixed Hammerstein type ⋮ A modification of Cauchy's method for quadratic equations ⋮ A new semilocal convergence theorem for Newton's method ⋮ Robust estimation and testing for general nonlinear regression models ⋮ The Ulm method under mild differentiability conditions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On convergence of the modified Newton's method under Hölder continuous Fréchet derivative ⋮ Toward a unified theory for third \(R\)-order iterative methods for operators with unbounded second derivative ⋮ A Newton-like iterative process for the numerical solution of Fredholm nonlinear integral equations ⋮ Solving a special case of conservative problems by secant-like methods ⋮ A convergence theorem for Newton-like methods under generalized Chen- Yamamoto-type assumptions

Uses Software

• PITCON

Cites Work

• On the approximation of some nonlinear equations
• Error analysis for the Newton-Raphson method
• Newton's method under mild differentiability conditions with error analysis

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