非线性方程组的非交替Newton-PHSS迭代法

Non-alternating Newton-PHSS iteration method for systems of nonlinear equations

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NewtonNPHSS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.

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.