孟玲玲^*

（  兰州大学数学与统计学院；  ）

摘要： 为了求解一种算子方程的Jacobi矩阵是正定矩阵的非线性方程组，本文将经典的Newton法和PSS迭代法相结合，得到了一种实用的不精确牛顿法—Newton-PSS迭代法。一方面，理论上给出了这种不精确牛顿法在一定条件下的局部收敛性定理；另一方面，将该方法应用于一个二维的非线性对流扩散方程，从数值结果上可以看出本文提出的Newton-PSS 迭代法显著地优于Newton-SOR迭代法，从而说明了该方法具有可行性和有效性。
关键词： 非线性方程组；PSS迭代法；牛顿法；局部收敛性

Meng lingling^*

（  Mathematics and statistice of Lanzhou University；  ）

Abstract： By making use of the PSS iteration as the inner solver for the Newton method, we establish a class of Newton-PSS methods for solving large sparse systems of nonlinear equations with positive-definite Jacobian matrices at the solution points. For the inexact Newton methods, a local convergence theorem is proved under proper conditions, and numerical results are given to examine it feasibility and effectiveness. In addition, the advantages of the Newton-PSS methods markedly over the Newton-SOR methods is shown through solving systems of nonlinear equations arising from the finite difference discretization of a two-dimensional convection-diffusion equation perturbated by a nonlinear term.

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