摘要
利用矩阵对的广义奇异值分解 (GSVD) ,得到了L非空的一个充分必要条件 ,并给出了问题P的解的表示。问题P 给定A∈Rm×n,B∈Rp×q,C∈Rm×t,D∈Rl×q,F∈Rm×q,设L ={ [X ,Y]:X∈Rn×p,Y ∈Rt×l,AXB+CYD =F} ,求 [^X ,^Y]∈L ,使得‖ [^X ,^Y]‖ =(‖ ^X‖2 +‖ ^Y‖2 ) 12
By applying the GSVD(generalized singular value decompositions) of matrix pairs,the necessary and sufficient conditions,under which Lis nonempty,are studied.The expressions for the solutions of Problem P is given. Problem P.Given A∈R m×n ,B∈R p×q ,C∈R m×t ,D∈R l×q ,F∈R m×q Let L=｛[X,Y]:X∈R n×p ,Y∈R t×l ,AXB+CYD=F｝,find [,]∈L such that ‖[,]‖=(‖‖ 2+‖‖ 2) 12 = min
出处
《华东船舶工业学院学报》
EI
2001年第3期34-37,共4页
Journal of East China Shipbuilding Institute(Natural Science Edition)
关键词
矩阵方程
广义奇异值分解
极小范数解
matrix equation
generalized singular value decomposition
minimum norm solution
