The Hermitian and skew-Hermitian splitting (HSS) method is an unconditionally convergentiteration method for solving large sparse non-Hermitian positive definite system oflinear equations.By making use of the HSS iteration as the inner solver for the Newtonmethod,we establish a class of Newton-HSS methods for solving large sparse systems ofnonlinear equations with positive definite Jacobian matrices at the solution points.For thisclass of inexact Newton methods,two types of local convergence theorems are proved underproper conditions,and numerical results are given to examine their feasibility and effectiveness.In addition,the advantages of the Newton-HSS methods over the Newton-USOR,the Newton-GMRES and the Newton-GCG methods are shown through solving systemsof nonlinear equations arising from the finite difference discretization of a two-dimensionalconvection-diffusion equation perturbed by a nonlinear term.The numerical implementationsalso show that as preconditioners for the Newton-GMRES and the Newton-GCGmethods the HSS iteration outperforms the USOR iteration in both computing time anditeration step.
