中文摘要：

为了求解矩阵范数约束下矩阵方程AX=B的最小二乘解问题，提出了一种迭代算法。该算法以广义Lanczos信赖域算法为基本框架，弥补了其不能求解矩阵方程的缺陷。数值实验表明，该算法是有效的。

英文摘要：

Aiming at the least-squares solutions of the matrix equation AX= B an iterative method is proposed. This method uses the general Lanczos trust under the norm inequality constraint, region algorithm as the frame method and remedies its defect on solving the matrix equation. Numerical experiments illustrate that the algorithm is effectire.