A construction procedure of iterative methods with cubical convergence

DOI10.1016/S0096-3003(96)00134-8zbMath0879.65035MaRDI QIDQ1366828

Miguel A. Hernández, José Manuel Gutiérrez Jimenez, José Antonio Ezquerro

Publication date: 22 January 1998

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

zbMATH Keywords

numerical examplesChebyshev methodcontinuation methoditerative methodserror estimateBanach spacenonlinear operator equationsconvergence acceleration of Newton's methodKantorovich-type convergence analysis

Mathematics Subject Classification ID

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

Related Items (9)

Application of iterative processes of \(R\)-order at least three to operators with unbounded second derivative ⋮ Semilocal convergence of a continuation method with Hölder continuous second derivative in Banach spaces ⋮ A CONTINUATION METHOD AND ITS CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS IN BANACH SPACES ⋮ Convergence of a parameter based iterative method for solving nonlinear equations in Banach spaces ⋮ Solving a nonlinear equation by a uniparametric family of iterative processes ⋮ Convergence of a continuation method under Lipschitz continuous derivative in Banach spaces ⋮ On the error estimates of several Newton-like methods ⋮ A construction procedure of iterative methods with cubical convergence. II: Another convergence approach ⋮ A NOTE ON THE SEMILOCAL CONVERGENCE OF CHEBYSHEV’S METHOD

Cites Work

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• Quadratic equations in Banach spaces
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• On Newton's method and nondiscrete mathematical induction
• Standard kantorovich theorem of the chebyshev method on complex plane
• A family of chebyshev-halley type methods
• Accessibility Of Solutions By Newton's Method
• A Unified Convergence Theory for a Class of Iterative Processes

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