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

作　　者：顾超 王珏钰 朱德通[2] Chao GU;Jue Yu WANG;De Tong ZHU(School of Statistics and Mathematics,Shanghai Lixin University of Accounting and Finance,Shanghai 201209,P.R.China;Mathematics and Science College,Shanghai Normal University,Shanghai 200234,P.R.China)

机构地区：[1]上海立信会计金融学院统计与数学学院,上海201209 [2]上海师范大学数学系,上海200234

出　　处：《数学学报（中文版）》2023年第2期317-338,共22页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11971302)。

摘　　要：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.

关 键 词：不精确牛顿法 牛顿—克雷洛夫子空间方法 全局收敛性 兰索斯方法 对称非线性方程组 

分 类 号：O221.2[理学—运筹学与控制论]