计算机工程与应用Issue(5)：65-70,6.DOI:10.3778/j.issn.1002-8331.1305-0215
矩阵方程 AXB+CYD=E最佳逼近自反解的迭代算法
Iterative algorithm for optimal approximation reflexive solutions of matrix equations AXB+CYD=E
摘要
Abstract
The iterative algorithm can be used to calculate the optimal approximation reflexive solutions of the Sylvester matrix equations AXB+CYD=E by using the hybrid steepest descent method. But the convergent speed of the algorithm is very slow. So it presents an iterative algorithm by using the conjugate direction method. Whatever matrix equations AXB+CYD=E are consistent or not, for arbitrary initial reflexive matrix X1 and Y1 , the optimal approximation reflexive solutions can be obtained within finite iteration steps by using the given algorithm. Two numerical examples show that the proposed algorithm is efficient, and the convergent speed is faster.关键词
Sylvester矩阵方程/Kronecker积/最佳逼近/自反矩阵/共轭方向Key words
Sylvester matrix equations/Kronecker product/optimal approximation/reflexive matrix/conjugate direction分类
数理科学引用本文复制引用
杨家稳,孙合明..矩阵方程 AXB+CYD=E最佳逼近自反解的迭代算法[J].计算机工程与应用,2015,(5):65-70,6.基金项目
安徽省高校省级自然科学基金（No.KJ2011B119）。 （）
