A unified approach for the convergence of certain numerical algorithms, using recurrent functions

DOI10.1007/S00607-010-0113-0zbMath1214.65027OpenAlexW1974161693MaRDI QIDQ605045

Saïd Hilout, Ioannis K. Argyros

Publication date: 23 November 2010

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-010-0113-0

zbMATH Keywords

numerical exampleserror boundsnonlinear equations in Banach spacesboundary value problemsemilocal convergenceroots of polynomialsnonlinear PDEGreen functionintegral equation methodNewton-like methodsmajorizing sequenceNewton-Kantorovich hypothesis

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Integral representations of solutions to PDEs (35C15) Numerical solutions to equations with nonlinear operators (65J15) Boundary element methods for boundary value problems involving PDEs (65N38) Numerical computation of roots of polynomial equations (65H04)

Related Items (1)

Extending the applicability of Newton's method for \(k\)-Fréchet differentiable operators in Banach spaces

Uses Software

• NewtonLib

Cites Work

• Unnamed Item
• Unnamed Item
• A note on Newton type iterative methods
• On a class of Newton-like methods for solving nonlinear equations
• A convergence theorem for Newton-like methods in Banach spaces
• Unified error analysis for Newton-type methods
• Convergence of Newton-like methods for singular operator equations using outer inverses
• Concerning the ``terra incognita between convergence regions of two Newton methods
• On the Newton-Kantorovich hypothesis for solving equations
• On an iterative algorithm of order 1.839… for solving nonlinear operator equations^∗)
• Convergence and Applications of Newton-type Iterations
• 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
• Majorizing Sequences and Error Bounds for Iterative Methods
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• A Unified Convergence Theory for a Class of Iterative Processes

This page was built for publication: A unified approach for the convergence of certain numerical algorithms, using recurrent functions