A generalized conjugate gradient, least square method
Numerische Mathematik
Iterative solution methods
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 convergence of parallel chaotic nonlinear multisplitting Newton-type methods
Journal of Computational and Applied Mathematics
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations
Applied Numerical Mathematics
Convergence of a generalized MSSOR method for augmented systems
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
Based on separable property of the linear and the nonlinear terms and on the Hermitian and skew-Hermitian splitting of the coefficient matrix, we present the Picard-HSS and the nonlinear HSS-like iteration methods for solving a class of large scale systems of weakly nonlinear equations. The advantage of these methods over the Newton and the Newton-HSS iteration methods is that they do not require explicit construction and accurate computation of the Jacobian matrix, and only need to solve linear sub-systems of constant coefficient matrices. Hence, computational workloads and computer memory may be saved in actual implementations. Under suitable conditions, we establish local convergence theorems for both Picard-HSS and nonlinear HSS-like iteration methods. Numerical implementations show that both Picard-HSS and nonlinear HSS-like iteration methods are feasible, effective, and robust nonlinear solvers for this class of large scale systems of weakly nonlinear equations.