对于一类矩阵方程组对称解的探索与实践  

Exploration and Practice of the Symmetric Solutionsof a Type of Matrix Equations

作　　者：吕睿星 孙王杰[1] 马俊 Lü Ruixing;SUN Wangjie;MA Jun(School of Science,Jilin Institute of Chemical Technology,Jilin 132022,China)

机构地区：[1]吉林化工学院理学院,吉林吉林132022

出　　处：《吉林化工学院学报》2022年第1期72-75,共4页Journal of Jilin Institute of Chemical Technology

摘　　要：约束矩阵方程组在振动理论、结构设计、系统辨识、数学控制理论、振动理论、地质学等诸多领域中有重要的应用价值.分析了矩阵方程组M_(1)Y_(1)N_(1)+M_(2)Y_(2)N_(2)=P_(1),M_(3)Y_(1)N_(3)+M_(4)Y_(2)N_(4)=P_(2)对称解的迭代算法,使用该算法能够自动判断对称解的情况.当矩阵方程组相容时,能够得到矩阵方程组的对称解.Constrained matrix equations have important applications in vibration theory,structural design,system identification,mathematical control theory,vibration theory,geology and many other fields.In this paper,the iterative method for symmetric solutions of matrix equations M_(1)Y_(1)N_(1)+M_(2)Y_(2)N_(2)=P_(1),M_(3)Y_(1)N_(3)+M_(4)Y_(2)N_(4)=P_(2) is analyzed.When the matrix equations are consistent,the symmetric solutions of the matrix equations can be obtained.

关 键 词：矩阵方程组 对称解 迭代法 

分 类 号：O241.6[理学—计算数学]