Iterative methods for nonlinear operator equations
type: Item
instance of: scholarly article
title: Iterative methods for nonlinear operator equations
zbMATH Open document ID: 0760.65055
DOI: 10.1016/0096-3003(92)90072-9
author: Zahari Zlatev
author: Anthony T. Chronopoulos
published in: Applied Mathematics and Computation
publication date: 1993-01-17T00:00:00Z
review text: The authors present a nonlinear extension of the conjugate gradient method applied to the normal equations. It is assumed that the Jacobian and the Hessian of the nonlinear operator are uniformly bounded. Global and local convergence results for the nonlinear algorithms are proved and asymptotic steplength estimates and error bounds are given. No numerical examples.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 96925
zbMATH Keywords: nonlinear operator equations
zbMATH Keywords: Hilbert space
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: normal equations
zbMATH Keywords: local convergence
zbMATH Keywords: asymptotic steplength estimates
zbMATH Keywords: error bounds
MaRDI profile type: Publication
full work available at URL: 0096-3003(92)90072-9
OpenAlex ID: W1977687488
cites work: A Taxonomy for Conjugate Gradient Methods
cites work: The N‐Step Iteration Procedures
cites work: The Conjugate Gradient Method for Linear and Nonlinear Operator Equations
cites work: On the Approximate Minimization of Functionals
cites work: Inexact Newton Methods
cites work: Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
cites work: Function minimization by conjugate gradients
cites work: Q3882253
cites work: Convergence of a two-stage Richardson process for nonlinear equations
cites work: Methods of conjugate gradients for solving linear systems
cites work: On General Iterative Methods for the Solutions of a Class of Nonlinear Operator Equations
cites work: Q5528974
cites work: Q5527119
cites work: A discrete Newton algorithm for minimizing a function of many variables
description: scientific article; zbMATH DE number 96925