求解张量绝对值方程的两步非精确Levenberg-Marquardt算法  

Two-step Inexact Levenberg-Marquardt Method for Tensor Absolute Value Equation

作　　者：马昌凤 谢亚君 MA Changfeng;XIE Yajun(Key Laboratory of Digital Technology and Intelligent Computing,School of Big Data,Fuzhou University of International Studies and Trade,Fuzhou 350202,China)

机构地区：[1]福州外语外贸学院大数据学院数字技术与智能计算重点实验室,福建福州350202

出　　处：《山西大学学报（自然科学版）》2023年第3期585-591,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11901098);福建省自然科学基金(2019J01879,2020J05034);福建省重大教改项目(FBJG20200310);新工科研究与改革实践项目(J1593419745784GS)。

摘　　要：张量绝对值方程可以重构为张量互补问题来求解。针对重构的张量互补问题,提出了两步非精确Levenberg-Marquardt (LM)算法,并给出了LM参数μk的一个新的选取方式,同时证明了所提出算法的收敛性定理。一些数值实例被测试,实验结果表明该算法是有效的。The tensor absolute value equation can be reconstructed into the tensor problem complementary.In this paper,for the con‐structed tensor complementary problem,two-step inexact Levenberg-Marquardt(LM)algorithm was proposed.And a new selection method of LM parameterμk was given.The convergence theorem of the proposed algorithm was proven.Some numerical examples were tested.Numerical results showed that the algorithm is effective.

关 键 词：张量绝对值方程 两步非精确LM算法 收敛性定理 数值实验 

分 类 号：O241[理学—计算数学]