Research On Solutions Of Different Types Of Constrained For Several Types Of Matrix Equations

The problem of solving matrix equations is one of the important research topics of numerical algebra.In recent years,with the development of control theory and matrix theory,the application of matrix equation constrained solutions has become more extensive,which has both theoretical and practical research significance.Constrained solutions of matrix equations include homogeneous constrained solutions and different constrained solutions.So far,many results have been achieved in the research on the homogeneous constrained solutions of matrix equations,while the research on the different constrained solutions of matrix equations is relatively small.Therefore,this paper studies the different constrained solutions of several different types of matrix equations.Firstly,based on the compatibility of a class of Sylvester matrix equations,an adaptive conjugate gradient algorithm is proposed to solve the reflexive and bisymmetric constrained least squares solution of the Sylvester matrix equation,and further solve the given matrix in the the optimal approximation problem in the set of constrained solutions of matrix equations.Numerical experimental results show that the algorithm is feasible and effective.Secondly,for a class of generalized periodic coupled Sylvester matrix equations different constrained solution problem,on the basis of the conjugate gradient algorithm for solving different constrained solutions of matrix equations,combined with the period of the matrix equation,an iterative algorithm for solving the real matrix and symmetric matrix constrained solutions of the matrix equation is established.Numerical experimental results show that the algorithm is feasible and effective.Finally,using an iterative algorithm similar to solving a class of generalized periodic coupled Sylvester matrix equations,the real matrix and symmetric matrix constrained solutions of a class of discrete-time periodic Sylvester matrix equations are studied,and numerical experiments are used to verify the feasibility and effectiveness of the algorithm.For the different constrained solutions of matrix equations,there are still many problems worthy of further study.At the end of the thesis,the next step is given.