A new sparsity preserving quasi-Newton update for solving nonlinear equations
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Numerical Analysis
A view of unconstrained optimization
Optimization
Comparing algorithms for solving sparse nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
Inexact trust region method for large sparse systems of nonlinear equations
Journal of Optimization Theory and Applications
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
A uniformly convergent finite difference scheme for a singularly perturbed semilinear equation
SIAM Journal on Numerical Analysis
On a numerical method for discrete analogues for boundary value problems
Nonlinear Analysis: Theory, Methods & Applications
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Journal of Computational and Applied Mathematics
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This paper proposes a new Newton-like method which defines new iterates using a linear system with the same coefficient matrix in each iterate. while the correction is performed on the right-hand-side vector of the Newton system. In this way a method is obtained which is less costly than the Newton method and faster than the fixed Newton method. Local convergence is proved for nonsingular systems. The influence of the relaxation parameter is analyzed and explicit formulae for the selection of an optimal parameter are presented. Relevant numerical examples are used to demonstrate the advantages of the proposed method.