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

Ai-Li Yang; Yu-Jiang Wu

doi:10.3934/naco.2012.2.839

Article Contents

2012, Volume 2, Issue 4: 839-853. Doi: 10.3934/naco.2012.2.839

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

Ai-Li Yang^1, and
Yu-Jiang Wu^1,

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

Received: December 2011

Revised: August 2012

Published: October 2012

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Abstract

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.

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Mathematics Subject Classification: Primary: 65H10,65F10; Secondary: 65H20.

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