一种解非线性方程组的不精确牛顿——兰索斯方法

An Inexact Newton-Lanczos Method for Solving a System of Nonlinear Equations

本文提出一种不完全线搜索技术的不精确牛顿—克雷洛夫(Newton-Krylov)子空间方法解对称非线性方程组,其中克雷洛夫子空间方法采用的是兰索斯(Lanczos)类分解技术.迭代方向是通过使用兰索斯方法近似求解非线性方程组的牛顿方程获得的.在合理的假设条件下,分析了算法的全局收敛性和局部超线性收敛速率.最后,数值结果显示了该算法的有效性.

We present an inexact Newton-Krylov subspace method with incomplete line search technique for solving symmetric nonlinear equations,in which the Krylov subspace method uses the Lanczos-type decomposition technique.The iterative direction is obtained by approximately solving the Newton’s equations of the nonlinear equations using the Lanczos method.The global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions.Finally,the numerical results show the effectiveness of the proposed algorithm.