信赖域方法在Hölderian局部误差界下的收敛性质  

ON THE CONVERGENCE OF THE TRUST REGION METHOD UNDER THE HÖLDERIAN ERROR BOUND CONDITION

作　　者：马积瑞 范金燕 Ma Jirui;Fan Jinyan(School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China;School of Mathematical Sciences,and MOE-LSC,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学数学科学学院,教育部科学工程计算重点实验室,上海200240

出　　处：《计算数学》2021年第4期484-492,共9页Mathematica Numerica Sinica

基　　金：国家自然科学基金(11971309)资助。

摘　　要：信赖域方法是求解非线性方程组的一种重要方法.本文研究了求解非线性方程组的信赖域半径趋于零的信赖域算法在Jacobi矩阵Hölderian连续条件下的全局收敛性质,以及其在Hölderian局部误差界和Jacobi矩阵Hölderian连续条件下的收敛速度.The trust region method is an improtant method for solving nonlinear equations.In this paper,we study the global convergence of the trust region method with trust region converging to zero under the Hölderian continuousness of the Jacobian.The convergence rate of the method is also given under the Hölderian error bound condition.

关 键 词：非线性方程组 信赖域方法 Hölderian局部误差界 

分 类 号：O241.7[理学—计算数学]