求解张量绝对值方程基于连续时间的神经网络方法  

THE CONTINUOUS-TIME NEURAL METWORK METHOD FOR TENSOR ABSOLUTE VALUE EQUATION

作　　者：马昌凤 谢亚君 Ma Changfeng;Xie Yajun(School of Big Data&Key Laboratory of Data Science and Intelligent Computing,Fuzhou University of International Studies and Trade,Fuzhou 350202)

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,福州350202

出　　处：《高等学校计算数学学报》2023年第1期84-96,共13页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(11901098);福建省自然科学基金(2020J05034)。

摘　　要：1引言考虑如下的张量绝对方程(TAVE):寻找向量x∈R^(n)满足Ax^(m-1)-B|x|^(m-1)=b,(1.1)其中A,B∈T(m,n)且m为偶数,b∈R^(n)为已知向量.这里T(m,n)表示m阶n维实张量的集合,向量|x|定义为|x|=(|x_(1)|,|x_(2)|,…,|x_(n)|)^(T).当m=2时,方程(1.1)退化为下面的(矩阵)绝对值方程(AVE):Ax-B|x|=b.(1.2)方程(1.2)的一个特例是当B为单位矩阵的情形,即Ax-|x|=b.(1.3).In this paper,the tensor absolute value equation is reconstructed into tensor complementary problem by introducing complementary function,and its key properties are analyzed.For the constructed tensor complementary problem,a continuous-time neural network method(CTNN) was proposed and the convergence theorem is proved.Some numerical results were reported.Numerical results show that the proposed algorithm is robust and effective.

关 键 词：单位矩阵 绝对值方程 张量 N维 神经网络方法 

分 类 号：O241[理学—计算数学]