摘要
本文主要讨论主子阵约束下矩阵方程AX=B的对称最小二乘解．基于投影定理,巧妙的把最小二乘问题转化为等式问题求解,并利用奇异值分解的方法,给出了该对称最小二乘解的一般表达式．此外,文章还考虑了此对称最小二乘解集合对任一给定矩阵的最佳逼近问题,得到了最佳逼近解,并给出了相应的算法步骤和数值例子．
This paper mainly discusses the symmetric least-squares solutions of matrix equation AX = B with a submatrix constraint. Based on the projection theorem, the least-squares problem is transformed into an equation problem. And by using the method of singular value decomposition（SVD）, the general expression of the symmetric least-squares solutions is obtained. Furthermore, to an given matrix, the optimal approximation problem in the solution set is considered.As for this problem, the optimal approximation solution, a numerical algorithm and a numerical example are provided.
出处
《数值计算与计算机应用》
CSCD
2006年第2期154-160,共7页
Journal on Numerical Methods and Computer Applications
基金
国家自然科学基金资助项目(10571047)
