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计算数学  2014 

基于交替投影算法求解单变量线性约束矩阵方程问题

, PP. 143-162

Keywords: 线性矩阵方程,交替投影算法,Dykstra&rsquo,s交替投影算法,最佳逼近问题,Krylov子空间方法

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Abstract:

研究如下线性约束矩阵方程求解问题:给定A×Rm×n,B×Rn×p和C×Rm×p,求矩阵X×R?Rn×n得A×B=C以及相应的最佳逼近问题,其中集合R为如对称阵,Toeplitz阵等构成的线性子空间,或者对称半(ε)正定阵,(对称)非负阵等构成的闭凸集.给出了在相容条件下求解该问题的交替投影算法及算法收敛性分析.通过大量数值算例说明该算法的可行性和高效性,以及该算法较传统的矩阵形式的Krylov子空间方法(可行前提下)在迭代效率上的明显优势,本文也通过寻求加速技巧进一步提高算法的收敛速度.

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