Convergence and uniqueness properties of Gauss-Newton's method
type: Item
instance of: scholarly article
title: Convergence and uniqueness properties of Gauss-Newton's method
zbMATH Open document ID: 1076.65053
DOI: 10.1016/S0898-1221(04)90086-7
author: C. Li
author: Wen-Hong Zhang
author: Xiao-Qing Jin
publication date: 2005-03-08T00:00:00Z
review text: The problem is to find a generalized solution for the equation \[ f(x)= 0,\tag{1} \] where \(f: \mathbb{R}^n\to \mathbb{R}^m\) is a nonlinear Fréchet-differentiable mapping and \(m\geq n\). The authors investigate the convergence of the Gauss-Newton method \[ x_{n+1}= x_n- [f'(x_n)^T f'(x_n)]^{-1} f'(x_n)^T f(x_n),\quad n= 0,1,2,\dots\tag{2} \] for finding the least squares solution to (2) under generalized Lipschitz conditions with \(L\) average. Some convergence theorems are proved as well as estimates for radius of the convergence ball and the uniqueness ball of the solution of (1) are derived. Some earlier and recent results are extended and improved sharply.
reviewed by: Otu Vaarmann
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 2142367
zbMATH Keywords: nonlinear least squares problem
zbMATH Keywords: Gauss-Newton's method
zbMATH Keywords: Lipschitz conditions with \(L\) average
zbMATH Keywords: convergence ball
zbMATH Keywords: uniqueness ball
MaRDI profile type: Publication
cites work: Q5787268
cites work: Q3943431
cites work: Convergence and Complexity of Newton Iteration for Operator Equations
cites work: Q4720691
cites work: Q4346546
cites work: Convergence of Newton's method and uniqueness of the solution of equations in Banach space
cites work: On the Continuity of the Generalized Inverse
cites work: Perturbation theory for pseudo-inverses
cites work: Convergence of Newton's method and uniqueness of the solution of equations in Banach spaces. II
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2142367