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

作　　者：杨家稳[1] 孙合明[2] 

机构地区：[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

出　　处：《计算机工程与应用》2015年第5期65-70,共6页Computer Engineering and Applications

基　　金：安徽省高校省级自然科学基金(No.KJ2011B119)

摘　　要：利用复合最速下降法的迭代算法能够求出矩阵方程AXB+CYD=E的最佳逼近自反解,但其收敛速度很慢。针对这一问题,提出一种利用共轭方向法的迭代算法。对于任给初始自反矩阵X1和Y1,无论矩阵方程AXB+CYD=E是否相容,该算法都可以经过有限次迭代计算出其最佳逼近自反解。两个数值例子表明该算法是可行的,且收敛速度更快。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 

分 类 号：O24[理学—计算数学]