中文摘要：

借鉴求线性矩阵方程组（LMEs）同类约束最小二乘解的修正共轭梯度法,建立了求双变量LMEs的一种异类约束最小二乘解的修正共轭梯度法,并证明了该算法的收敛性.在不考虑舍入误差的情况下,利用该算法不仅可在有限步计算后得到LMEs的一组异类约束最小二乘解,而且选取特殊初始矩阵时,可求得LMEs的极小范数异类约束最小二乘解.另外,还可求得指定矩阵在该LMEs的异类约束最小二乘解集合中的最佳逼近.算例表明,该算法是有效的.

英文摘要：

Based on the modified conjugate gradient method for same constrained least square solution of the linear matrix equations, a modified conjugate gradient method is constructed for different constrained least square solution of the linear matrix equations with two variables. And the convergence of this method can be proved. By this method, a different constrained least square solution can be obtained within finite iterative steps in absence of roundoff errors, and the different constrained least square solution with leastnorm can be got by choosing special initial matrices. In addition, the optimal approximation matrix to any given matrix can be obtained in the set of the different constrained least square solutions. Examples show that the method is efficient.