Convergence behaviour of inexact Newton methods
Mathematics of Computation
Methods for Solving Systems of Nonlinear Equations
Methods for Solving Systems of Nonlinear Equations
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
A choice of forcing terms in inexact Newton method
Journal of Computational and Applied Mathematics
A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations
Applied Numerical Mathematics
Local convergence of inexact methods under the Hölder condition
Journal of Computational and Applied Mathematics
Convergence behaviour of inexact Newton methods under weak Lipschitz condition
Journal of Computational and Applied Mathematics
Local convergence analysis of inexact Newton-like methods under majorant condition
Computational Optimization and Applications
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The modified Newton-HSS method, which is constructed by employing the Hermitian and skew-Hermitian splitting methods as the inner iteration process at each step of the outer modified Newton's iteration, has been proved to be a competitive method for solving large sparse systems of nonlinear equations with non-Hermitian positive-definite Jacobian matrices. In this paper, under the hypotheses that the derivative is continuous and the derivative satisfies the Holder continuous condition, two local convergence theorems are established for the modified Newton-HSS method. Furthermore, the rate of convergence of the modified Newton-HSS method is also characterized in terms of the rate of convergence of the matrix @?T(@a;x)@?. The numerical example is given to confirm the concrete applications of the results of our paper.