An improved convergence analysis of a one-step intermediate Newton iterative scheme for nonlinear equations

DOI10.1007/s12190-011-0476-1zbMath1295.65065OpenAlexW2008631855MaRDI QIDQ2511014

Ioannis K. Argyros, Livinus Ugochukwu Uko

Publication date: 5 August 2014

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

Full work available at URL: https://doi.org/10.1007/s12190-011-0476-1

zbMATH Keywords

numerical exampleNewton's methodmajorant methodLipschitz conditionnonlinear operator equationsiterative solutionmajorizing sequencecenter-Lipschitz conditionKantorovich theoremZabrejko-Nguen conditionsintermediate Newton scheme

Mathematics Subject Classification ID

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

Related Items

Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extending the Newton-Kantorovich hypothesis for solving equations
• General local convergence theory for a class of iterative processes and its applications to Newton's method
• On the Newton-Kantorovich hypothesis for solving equations
• A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
• New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
• Convergence and Applications of Newton-type Iterations
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• On the Two‐step Newton Method for the Solution of Nonlinear Operator Equations