中文摘要：

大型稀疏非Hermite正定Jacobi矩阵对应的非线性方程组的迭代求解历来受到重视．结合不精确Newton法和非交替PHSS迭代法，提出了迭代求解非线性方程组的Newton-NPHSS方法，给出了迭代法的局部收敛定理，并演算了数值例子，阐明了Newton—NPHSS是有效的迭代法．

英文摘要：

Much attention has been paid on the iteration solution for large scale and sparse systems of nonlinear equations whose Jacobian matrix is non-Hermitian positive definite during these years. Our goal in this paper is to combine the inexact Newton method with non-alternating preconditioned Hermitian and skew- Hermitian splitting （PHSS） iteration method, and to present a non-alternating Newton-PHSS （Newton-NPHSS） iteration method for solving systems of nonlinear equations. Local convergence theorem of the method is given. Numerical examples are carried out to verify the effectiveness of Newton-NPHSS method.