求解Hankel张量方程的修正自适应LM算法  

The modified adaptive LM algorithm for solving Hankel tensor equation

作　　者：马昌凤 李清雅 MA Chang-feng;LI Qing-ya(School of Big Data&Key Laboratory of Digital Technology and Intelligent Computing,Fuzhou University of International Studies and Trade,Fuzhou 350202,China;School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China)

机构地区：[1]福州外语外贸学院大数据学院&数据科学与智能计算重点实验室,福建福州352002 [2]福建师范大学数学与统计学院,福建福州350117

出　　处：《高校应用数学学报（A辑）》2024年第1期64-72,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(12371378);福建省自然科学基金(2023J011127)。

摘　　要：结合经典的LM算法及其变形,提出了求解Hankel张量方程的修正自适应LM算法,并证明其全局收敛性和局部二次收敛性.数值实验验证了所提算法的可行性和有效性.In this paper,combined with classic LM method and its variant,a modified adaptive LM algorithm is proposed for solving Hankel tensor equation.It is proved that this method has global convergent and local quadratic convergence.Numerical experiments show that the method is feasible and effective.

关 键 词：Hankel张量方程 修正自适应LM算法 收敛性分析 数值实验 

分 类 号：O241.7[理学—计算数学]