# American Institute of Mathematical Sciences

2012, 2(4): 839-853. doi: 10.3934/naco.2012.2.839

## Newton-MHSS methods for solving systems of nonlinear equations with complex symmetric Jacobian matrices

 1 School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China, China

Received  December 2011 Revised  August 2012 Published  November 2012

Modified Hermitian and skew-Hermitian splitting (MHSS) method is an unconditionally convergent iterative method for solving large sparse complex symmetric systems of linear equations. By making use of the MHSS iteration as the inner solver for the inexact Newton method, we establish a class of inexact Newton-MHSS methods for solving large sparse systems of nonlinear equations with complex symmetric Jacobian matrices at the solution points. The local and semi-local convergence properties are analyzed under some proper assumptions. Moreover, by introducing a backtracking linear search technique, a kind of global convergence inexact Newton-MHSS methods are also presented and analyzed. Numerical results are given to examine the feasibility and effectiveness of the inexact Newton-MHSS methods.
Citation: Ai-Li Yang, Yu-Jiang Wu. Newton-MHSS methods for solving systems of nonlinear equations with complex symmetric Jacobian matrices. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 839-853. doi: 10.3934/naco.2012.2.839
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