牛顿迭代法在非线性特征问题中的收敛性

摘要

Positive solutions of nonlinear eigen-problem with irreducible Z-matrix are studied.Firstly,theories of Z-matrix and fixed point theorem are adopted.Some sufficient conditions are given which guarantee that the nonlinear eigen-problem with irreducible Z-matrix has a unique positive eigenvector.Secondly,the Newton iterative method is constructed for numerically solving such a positive eigenvector,and its convergence is proved.Last,a numerical example is presented to show the validity of the proposed algorithm.%研究具有不可约Z-矩阵结构的非线性特征问题的正解.采用Z-矩阵理论及不动点定理,给出具有不可约Z-矩阵结构的非线性特征方程正特征向量的存在性及唯一性的充分条件.构建数值求解此正特征向量的牛顿迭代法,并证明所构建的算法收敛的.实验表明该算法有效.