The mathematics of nonlinear programming
The mathematics of nonlinear programming
The solution of two-point boundary value problems by the alternating group explicit (AGE) method
SIAM Journal on Scientific and Statistical Computing
Asymptotic mesh independence of Newton-Galerkin methods via a refined Mysovskii theorem
SIAM Journal on Numerical Analysis
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
On the formulation and theory of the Newton interior-point method for nonlinear programming
Journal of Optimization Theory and Applications
The two-stage arithmetic mean method
Applied Mathematics and Computation
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
On the Newton interior-point method for nonlinear programming problems
Journal of Optimization Theory and Applications
The Newton-arithmetic mean method for the solution of systems of nonlinear equations
Applied Mathematics and Computation
Numerical Analysis in Modern Scientific Computing: An Introduction
Numerical Analysis in Modern Scientific Computing: An Introduction
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Convergence behaviour of inexact Newton methods under weak Lipschitz condition
Journal of Computational and Applied Mathematics
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In this paper, we consider the Newton-iterative method for solving weakly nonlinear finite-difference systems of the form F(u)=Au+G(u)=0, where the jacobian matrix G'(u) satisfies an affine invariant Lipschitz condition. We also consider a modification of the method for which we can improve the likelihood of convergence from initial approximations that may be outside the attraction ball of the Newton-iterative method. We analyse the convergence of this damped method in the framework of the line search strategy. Numerical experiments on a diffusion-convection problem show the effectiveness of the method.