矩阵方程A^(T)XB+B^(T)X^(T)A=D子矩阵约束对称解的MCG算法  

MCG Algorithm for Symmetric Solutions of Matrix Equations A^(T)XB+B^(T)X^(T)A=D with Submatrix Constraints

作　　者：梁志艳 LIANG Zhiyan(Department of Basic Courses,Shanxi Engineering Vocational College,Taiyuan 030000,Shanxi)

机构地区：[1]山西工程职业学院基础部,山西太原030000

出　　处：《济源职业技术学院学报》2023年第3期50-54,共5页Journal of Jiyuan Vocational and Technical College

摘　　要：建立求矩阵方程A^(T)XB+B^(T)X^(T)A=D的子矩阵约束解的MCG算法。首先对矩阵作分块处理,将其转化为求一类双变量矩阵方程异类约束解的问题;其次,基于修正共轭梯度法,构造求其异类约束解和异类约束最小二乘解的迭代算法,该算法具有约束解存在性的判断功能;最后,证明算法的收敛性,并通过数值算例说明算法的有效性。This paper establishes the MCG algorithm for finding submatrix constraint solutions of matrix equations.Firstly,divide the matrix into blocks and transform it into a problem of solving a class of bivariate matrix equations with heterogeneous constraint;secondly,based on the modified conjugate gradient method,an iterative algorithm is constructed to obtain the solution of heterogeneous constraints and the least squares solution of heterogeneous constraints,which has the function of determining the existence of constraint solutions;finally,prove the convergence of the algorithm and demonstrate its effectiveness through numerical examples.

关 键 词：矩阵方程 子矩阵约束对称解 MCG算法 

分 类 号：O241.7[理学—计算数学]