线性矩阵方程组异类约束最小二乘解的迭代算法  

ITERATIVE METHOD FOR A DIFFERENT CONSTRAINED LEAST SQUARE SOLUTION OF LINEAR MATRIX EQUATIONS

作　　者：刘晓敏[1] 张凯院[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《高等学校计算数学学报》2013年第3期250-262,共13页Numerical Mathematics A Journal of Chinese Universities

摘　　要：用Rm×n表示m×n实矩阵集合，Based on the iterative method for same constrained least square so- lution of linear matrix equations an iterative method is constructed for different constrained least square solutions of linear matrix equations by constructing equiv- alent linear matrix equations. 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 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 that the method is efficient.

关 键 词：线性矩阵方程组 异类约束 最小二乘解 迭代算法 计算数学 

分 类 号：O1[理学—数学]