中文摘要：

通过构造等价的线性矩阵方程组（LMEs），将不相容的LMEs异类约束最小二乘解（Ls解）问题转化为相容的LMEs异类约束解问题，然后根据求LMEs的异类约束解的迭代算法构造原理，建立求LMEs的一种异类约束Ls解的迭代算法．不考虑舍入误差时，该算法可在有限步计算后求得LMEs的一组异类约束L8解；选取特殊的初始矩阵时，该算法可求得LMEs的极小范数异类约束Ls解．此外，还可在LMEs的异类约束Ls解集合中给出指定矩阵的最佳逼近矩阵．

英文摘要：

For the incompatible LMEs, we first construct its equivalent linear matrix equations, and then change the corresponding different constrained least square solution problem into the different constrained solution problem of the compatible LMEs. Finally, an iterative method is designed to find the different constrained least square solution based on the structure principle of an iterative method for LMEs. With this iterative method, the different constrained least square solution can be obtained within finite iteration steps in the absence of round off errors, and the different constrained least square solution with least-norm can be obtained by choosing a special initial matrix. In addition, the optimal approximation matrix to any given matrix can be found under the framework of the different constrained least square solutions.