### Iterative algorithm for optimal approximation reflexive solutions of matrix equations AXB+CYD=E

YANG Jiawen1, SUN Heming2

1. 1.Chuzhou Vocational and Technical College, Chuzhou, Anhui 239000, China
2.College of Science, Hohai University, Nanjing 211100, China
• Online:2015-03-01 Published:2015-04-08

### 矩阵方程AXB+CYD=E最佳逼近自反解的迭代算法

1. 1.滁州职业技术学院，安徽 滁州 239000
2.河海大学 理学院，南京 211100

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.