Inexact Newton method via Lanczos decomposed technique for solving box-constrained nonlinear systems  

作　　者：张勇 朱德通 

机构地区：[1]Mathematics and Science College,Shanghai Normal University [2]Business College,Shanghai Normal University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2010年第12期1593-1602,共10页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No. 10871130);the Ph. D.Programs Foundation of Ministry of Education of China (No. 20093127110005);the Shanghai Leading Academic Discipline Project (No. T0401)

摘　　要：This paper proposes an inexact Newton method via the Lanczos decomposed technique for solving the box-constrained nonlinear systems. An iterative direction is obtained by solving an affine scaling quadratic model with the Lanczos decomposed technique. By using the interior backtracking line search technique, an acceptable trial step length is found along this direction. The global convergence and the fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the results of the numerical experiments show the effectiveness of the pro- posed algorithm.This paper proposes an inexact Newton method via the Lanczos decomposed technique for solving the box-constrained nonlinear systems. An iterative direction is obtained by solving an affine scaling quadratic model with the Lanczos decomposed technique. By using the interior backtracking line search technique, an acceptable trial step length is found along this direction. The global convergence and the fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the results of the numerical experiments show the effectiveness of the pro- posed algorithm.

关 键 词：nonlinear system Lanczos decomposed technique inexact Newton method nonmonotonic technique 

分 类 号：O241.8[理学—计算数学]