约束矩阵方程线性约束逼近解交替投影方法研究  

Research on Alternating Projection Method of Linear Constrained Approximation Solution of Constrained Matrix Equation

作　　者：吴恒飞 张宗标 Wu Hengfei;Zhang Zongbiao(Bozhou College,Bozhou 236800,China)

机构地区：[1]亳州学院,安徽亳州236800

出　　处：《廊坊师范学院学报（自然科学版）》2021年第3期8-11,25,共5页Journal of Langfang Normal University(Natural Science Edition)

基　　金：安徽省高校自然科学研究项目(KJ2017A704);安徽省教学研究项目(2019jyxm0540);亳州学院精品课程《线性代数》(2017jpkc04);亳州学院教研项目(2017ybjy22);亳州学院重点科研项目(BYZ2019B03);亳州学院重点教学研究项目(2019zdjy06)。

摘　　要：为提高约束矩阵方程线性约束控制能力,构建约束矩阵方程线性约束逼近解交替投影机械模型。首先采用微分参数融合方法构建线性约束逼近特征分解模型,结合齐次双曲波动控制方法得到线性约束特征解,然后采用全局有限维特征解析控制的方法,确定线性平稳特征周期,并根据对合Cauchy-Hadamard稳定性的解析融合,实现对逼近解的自适应加权学习,建立正定对称矩阵,从而构建一类约束矩阵方程实现约束逼近解交替投影。通过证明可知,约束矩阵方程线性约束逼近解交替投影过程是稳态收敛的。In order to improve the linear constraint control ability of constraint matrix equation,this paper constructs an alternate projection mechanical model of linear constraint approximation solution of constraint matrix equation.First differential parameter fusion method was used to construct the linear constraint decomposition model approximation characteristics,combined with the feature of homogeneous hyperbolic wave control method for linear constraint solution,and then parse control method using global finite dimensional characteristics,determine the smooth linear characteristics of the cycle,and according to the convolution Cauchy-Hadamard stability analytical integration,realize the approximate solution of the adaptive weighted learning,and to establish a positive definite symmetric matrix,so as to construct a class of constrained matrix equation approximate solution alternating projection implementation constraints.It can be seen from the proof that the alternating projection process of the linear constraint approximation solution of the constraint matrix equation established in this study is steady-state convergence.

关 键 词：约束矩阵方程 线性约束逼近解 交替投影 自适应加权学习 

分 类 号：O175[理学—数学]