摘要
借鉴求线性矩阵方程(LME)同类约束最小二乘解的修正共轭梯度法,建立了求双变量LME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LME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LME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LME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.
Based on the modified conjugate gradient method, which gets same constrained least square solution of the linear matrix equation, a modified conjugate gradient method is constructed for different constrained least square solution of the linear matrix equation with two variables. And the convergence of this method is proved. By this method, a different constrained least square solution can be obtained within finite iterative steps in absence of round-off errors, and the different constrained least square solution with least-norm 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 the efficiency of the method.
出处
《中北大学学报（自然科学版）》
CAS
北大核心
2012年第4期358-362,386,共6页
Journal of North University of China(Natural Science Edition)
基金
国家自然科学基金资助项目(11071196)
关键词
线性矩阵方程
异类约束最小二乘解
修正共轭梯度法
极小范数解
最佳逼近
linear matrix equation
different constrained least square solution
modified conjugate gradient method
least-norm solution
optimal approximation
