The Symmetric Solutions Of Large Scale Of Linear Matrix Equations Based On Recursive Methods

Matrix equations is an important part of matrix analysis in Numerical Algebra and a problem needed to solve frequently in practice. The constrained matrix equations are interested by many authors. Over the years, the problems about matrix equations are addressed in many articles, and a variety of methods for solving these equations have become more and more perfect. There have been a lot of work on the studying for large matrix equations, such as Lyapunov linear matrix equations, Sylvester linear matrix equations and nonlinear algebraic Riccati equation, etc. However, the symmetric solutions of large scale of matrix equations have not been discussed before. This paper is concerned on the basis of previous research, and we study the symmetric solutions of two types of large scale of matrix equations with the recursive blocked mathod.The programming skills which program call itself is always called recursive, which usually translate a large and complex problem into smaller problems that similar to the original problem ring upon ring. In this pager, the recursive method is applied to solve matrix equations,the symmetric solutions of two types of matrix equations are discussed,and the main results are as follows:1. Basing on the real Schur decomposition of matrix and the use of recursive blocked mathod,the large scale of matrix equation AX=B is transformed into three small scale of matrix equations,we solve these equations and get the symmetric solution and symmetric least squares solution of the matrix equation AX=B,Furthermore,we give the numerical algorithms and examples to solve it.2. We research the symmetric soluton of the large scale of matrix equati-on AX+XAT=B with its coefficient matrix is narmal by using the recursive blocked method, Furthermore,we give the numerical algorithms and examples to solve it.3. We compare the algorithm which solve the symmetric solutions of these two type of matrix equations under recursive blocked method with the classical algorithm,and we get the better conclusion.