Semi-implicit method for long time scale magnetohydrodynamic computations in three dimensions
Journal of Computational Physics
Inexact trust region method for large sparse systems of nonlinear equations
Journal of Optimization Theory and Applications
A Globally Convergent Newton-GMRES Subspace Method for Systems of Nonlinear Equations
SIAM Journal on Scientific Computing
Numerical Methods
A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations
Applied Numerical Mathematics
A performance comparative study on the implementation methods for OFDMA cross-layer optimization
Future Generation Computer Systems
| Hi-index | 0.00 |
An iterative method for globally convergent solution of nonlinear equations and systems of nonlinear equations is presented. Convergence is quasi-monotonous and approaches second order in the proximity of the real roots. The algorithm is related to semi-implicit methods, earlier being applied to partial differential equations. It is shown that the Newton-Raphson and Newton methods are special cases of the method. The degrees of freedom introduced by the semi-implicit parameters are used to control convergence. When applied to a single equation, efficient global convergence and convergence to a nearby root makes the method attractive in comparison with methods as those of Newton-Raphson and van Wijngaarden-Dekker-Brent. An extensive standard set of systems of equations is solved and convergence diagrams are introduced, showing the robustness, efficiency and simplicity of the method as compared to Newton's method using linesearch.