一类矩阵方程的公共解  

COMMON SOLUTIONS OF THE MATRIX EQUATIONS

作　　者：陈兴同[1] 

机构地区：[1]中国矿业大学理学院数学系,徐州221008

出　　处：《高等学校计算数学学报》2005年第2期133-148,共16页Numerical Mathematics A Journal of Chinese Universities

摘　　要：1引言 对由A,B,C,D为系数矩阵而决定的多个矩阵方程AXC=E,BXD=F,AXD=G,BXC=H构成的矩阵方程组在相容及不相容情况下的公共解的讨论已经有好多成果,但都局限于两个矩阵方程的情况(文[1]、[2]、[4]、[5]、[8]、[9]);本文我们将利用矩阵对的广义奇异值分解GSVD讨论更一般的矩阵方程组(AXC,BXD,AXD)=(E,F,G)等及(AXC,BXD,AXD,BXC)=(E,F,G,H)在相容及不相容情况下的解.By applying the GSVD of matrix pairs,we discuss common solutions of the matrix equations AXC =E, BXD = F, AXD = G, BXC = H, under consistent and nonconsistent case respectively. We also discuss common symmetric solutions of the matrix equations AXXT = E, BXBT = F, AXBT = G, BXAT = H under consistent and nonconsistent case respectively. The necessary and sufficient conditions for the existence and the expressions of solutions of these matrix equations are provided.

关 键 词：矩阵方程 公共解 广义奇异值分解 数值计算 

分 类 号：O241.6[理学—计算数学]