中文摘要：

约束矩阵方程在自动控制理论、生物学、电学等领域有广泛的应用．本文研究了矩阵元素和特征值区间约束下矩阵方程AXB＋CYD—E最小二乘解问题．给出矩阵对（X＊，Y＊）是问题的解的充分必要条件，给出计算约束解的迭代方法，证明了算法的全局收敛性．

英文摘要：

The constraint matrix equation problems have been widely used in control theory, biology, electrici- ty and so on. In this paper, we solve the least squares problem of the matrix equation AXB ＋ CYD = E with the matrix element and eigenvalue interval constraints. The necessary and sufficient condition for matrix pair （X＊,Y＊ ） being a solution of the problem is derived. An iteration algorithm to solve the constraint solution is given, and the convergence of the algorithm is showed.