NGLM:一类全局收敛的Newton-GMRES方法

NGLM: A GLOBALLY CONVERGENT NEWTON-GMRES METHOD

本文提出了一类具有全局收敛性质的Newton-GMRES方法-NGLM方法.该方法是对经典Newton-GMRES方法的推广.NGLM方法的全局策略是当在非精确Newton 方向上后退不能成功时,转而在一个子空间上运用信赖域方法确定迭代步长.理论分析与数值实验均表明,NGLM方法改善了Newton-GMRES方法的强健性.

For large sparse system of nonlinear equations, we propose a globally convergent Newton-GMRES method, called as the Newton-GMRES with Levenberg-Marquardt strategy (NGLM) method. This method is a technical generalization of the standard Newton-GMRES method. In NGLM method, the adopted global strategy is using the trust region technique in a subspace to find a satisfactory iteration step when the backtracking along the inexact Newton direction fails. Both theoretical analysis and numerical results show that NGLM method is more robust than the Newton-GMRES method.