An Improved Convergence Analysis and Applications for Newton-Like Methods in Banach Space

DOI10.1081/NFA-120026364zbMath1040.47045MaRDI QIDQ4439615

Ioannis K. Argyros

Publication date: 14 December 2003

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

zbMATH Keywords

Newton-like methodChen-Yamamoto-type conditions

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) Methods of successive quadratic programming type (90C55)

Related Items

Approximating Solutions of Equations Using Two-Point Newton Methods ⋮ A Newton-like method for generalized operator equations in Banach spaces ⋮ An improved unifying convergence analysis of Newton's method in Riemannian manifolds ⋮ On a two-point Newton-like method of convergent order two ⋮ Concerning the ``terra incognita between convergence regions of two Newton methods ⋮ Majorizing sequences for Newton's method from initial value problems

Cites Work

• A note on Newton type iterative methods
• A convergence theorem for Newton-like methods in Banach spaces
• Local convergence of inexact Newton-like iterative methods and applications
• Local Convergence of Inexact Newton Methods
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• Convergence domains of certain iterative methods for solving nonlinear equations
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• On a new Newton-Mysovskii-type theorem with applications to inexact Newton-like methods and their discretizations
• A Unified Convergence Theory for a Class of Iterative Processes
• Unnamed Item
• Unnamed Item
• Unnamed Item