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A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations. (English) Zbl 1123.65040
A class of globally convergent inexact Newton methods, the Newton-GMRES with quasi-conjugate-gradient backtracking (NGQCGB) methods, for solving large sparse systems of nonlinear equations are presented. These methods can be considered as a suitable combination of the Newton-GMRES iteration and some efficient backtracking strategies. In some cases, known Newton-GMRES backtracking (NGB) methods stagnate for some iterations or even fail. To avoid this disadvantage of NGB methods the authors propose a new alternative strategy, called quasi-conjugate-gradient with backtracking (QCGB), using the known information such as the projection of the gradient of the merit function on a proper subspace and last nonlinear step. Numerical computations show that the NGQCGB method is more robust and efficient than both the NGB method and the Newton-GMRES with eqality curve backtracking (NGECB) method.
65H10Systems of nonlinear equations (numerical methods)