A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations

Authors:
Heng-Bin An;Zhong-Zhi Bai
Affiliations:
State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy o ...;State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy o ...
Venue:
Applied Numerical Mathematics
Year:
2007

Citing 16
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Abstract

The inexact Newton with backtracking (INB) method is a powerful tool for solving large sparse systems of nonlinear equations. In particular, if the generalized minimal residual (GMRES) method is used to solve the Newton equations, then the Newton-GMRES with backtracking (NGB) method is obtained. In this paper, we present a new class of globally convergent Newton-GMRES methods. In these methods, the typical backtracking strategy is augmented with a new strategy that is invoked when the inexact Newton direction is not satisfactory. Global convergence properties of the proposed methods are established and numerical results are provided, showing that the new method, called the Newton-GMRES with quasi-conjugate-gradient backtracking (NGQCGB), is very robust and effective.