一类广义Sylvester矩阵方程组对称解的MCG算法  

MCG Algorithm for Symmetric Solutions of a Class of Generalized Coupled Sylvester Equations

作　　者：陈世军 CHEN Shijun(Fuzhou Institute of Technology,Fuzhou 350015,China)

机构地区：[1]福州理工学院文理学院,福建福州350015

出　　处：《通化师范学院学报》2024年第4期15-22,共8页Journal of Tonghua Normal University

基　　金：2021年度福建省教育厅中青年教师教育科研项目(JAT210584);福州理工学院校级科研项目(FTKY2023006).

摘　　要：该文建立了求解一类广义Sylvester矩阵方程组对称解的修正共轭梯度算法(MCG算法),给出了MCG算法的性质和收敛性证明,在忽略舍入误差情况下,建立的MCG算法能在有限步迭代后得到该方程组的对称解.选取特殊初始矩阵时,可求得该方程组的极小范数对称解.任意给定初始矩阵,可以在约束解矩阵集合中求出给定初始矩阵的最佳逼近矩阵.数值算例验证了所建立算法的可行性.A modified conjugate gradient algorithm(MCG algorithm)was established in founding the symmetric solution of the generalized coupled Sylvester equation system.We give the properties and convergence proof of the MCG algorithm.When we ignore round off error,the MCG algorithm established in this paper can obtain the symmetric solution of the equation system after finite step iteration.When we select a special initial matrix,the minimum norm symmetric solution of the system of equations can be obtained.Given a known matrix,we can find the best approximation matrix for this matrix from a set of known solution matrices.Numerical experiments verify the feasibility of the algorithm proposed in the paper.

关 键 词：广义Sylvester矩阵方程组 修正共轭梯度算法 对称解 

分 类 号：O241.6[理学—计算数学]