Study On Solving Methods And Algorithms Of Some Special Matrix Equations

In this paper,the solutions and algorithms of some special matrix equations are studied.This paper mainly studied the special solutions and the inverse eigenvalue problems of matrix equations.This paper is divided into six parts.The first part is the introduction,which expounds the research background and present situation,the research content and the mark used of this paper.The second part,the special solutions of matrix equation AX=B are researched.The(skew-)Hermitian anti-reflexive solutions of AX=B are given by using matrix analysis method and Moore-Prose generalized inverse,and the related optimal approximation problem is discussed.If the matrix equation is inconsistent,the least squares(skew-)Hermitian anti-reflexive solutions are obtained by singular value decomposition.Finally,the algorithm and numerical calculation are given to verify the effectiveness of the research results in this section.The third part,the least squares {P,Q,k+1}-reflexive solution to matrix equation AXB=C is studied.The least squares {P,Q,k+1}-reflexive solution of AXB=C is obtained by generalized eigenvalue decomposition and generalized inverse.Finally,the algorithm and numerical calculation are given to verify the effectiveness of the research results in this section.The fourth part,the least squares solution of the matrix equation AXB+CXD=E for symmetric arrowhead with the minimum norm is studied.The constrained solution of matrix equation is extended to quaternion algebra,and the general solution of this problem is given by using Moore-Prose inverse and the Kronecker product.Finally,the algorithm and numerical calculation are given to verify the effectiveness of the research results in this section.The fifth part,the inverse eigenvalue problem and least squares problem of skew-Hermitian{P,k+1}-reflexive matrices are studied.Firstly,the necessary and sufficient conditions for the solvability and the general solution are presented by generalized inverse and the related optimal approximation problems are also given.Then,we obtain the least squares solution of AX=B satisfying the special condition by the singular value decomposition.Finally,the algorithm and numerical calculation are given to verify the effectiveness of the research results in this section.The sixth part is the conclusion,which summarizes the main work results of this paper.