数学理论与应用 ›› 2016, Vol. 36 ›› Issue (4): 29-35.

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求解单调非线性方程组的非精确正则化牛顿法及其局部收敛性

李维飞   

  1. 长沙理工大学数学与统计学院,长沙,410004
  • 出版日期:2016-12-30 发布日期:2020-09-25
  • 基金资助:

    湖南省教育厅项目(13B137);

    湖南省自然科学基金(14JJ3084)

An Inexact Regularized Newton Method for Monotone and Nonlinear Equations and its Local Convergence

Li Weifei   

  1. School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410014,China
  • Online:2016-12-30 Published:2020-09-25

摘要:

本文提出了一种求解单调非线性方程组的非精确正则化牛顿方法,在较弱的局部误差界条件下,证明了该方法具有局部二次收敛性,该方法是文献[4]中精确正则化牛顿法的推广.

关键词: 单调非线性方程组, 非精确正则化牛顿法, 局部收敛

Abstract:

This paper presents an inexact regularized Newton method for monotone and nonlinear equations. Under relatively weak local error bound conditions,we show that the proposed method converges quadratically.This method is a generalization of the exact regularized Newton method proposed by Fan and Yuan[4].

Key words:

"> Monotone nonlinear equations, Inexact regularized Newton method, Local convergence