An Iterative method for the Symmetric Solutions of the Linear Matrix Equations with Several Variables

摘要

In this paper, we consider an iterative method to find the symmetric solutions of the linear matrix equations with several variables and its convergence by applying the conjugate gradient method of solving linear algebraic equations and using special transformation and approximate disposal. Then we give the symmetric solution with least norm by choosing a special initial matrix. Moreover, an iterative algorithm is given for it and the numerical examples show that the algorithm is quite efficient.