A choice of forcing terms in inexact Newton method

Authors:
Heng-Bin An;Ze-Yao Mo;Xing-Ping Liu
Affiliations:
State Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, P.O. Box 8009, 100088, PR China;High Performance Computing Center, Institute of Applied Physics and Computational Mathematics, Beijing, P.O. Box 8009, 100088, PR China;State Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, P.O. Box 8009, 100088, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

Inexact Newton method is one of the effective tools for solving systems of nonlinear equations. In each iteration step of the method, a forcing term, which is used to control the accuracy when solving the Newton equations, is required. The choice of the forcing terms is of great importance due to their strong influence on the behavior of the inexact Newton method, including its convergence, efficiency, and even robustness. To improve the efficiency and robustness of the inexact Newton method, a new strategy to determine the forcing terms is given in this paper. With the new forcing terms, the inexact Newton method is locally Q-superlinearly convergent. Numerical results are presented to support the effectiveness of the new forcing terms.