This paper, considers the following two problerns: Problem Ⅰ Given A ∈ Rm×n,B ∈ Rp×q,C ∈ Rm×q,G ∈ Rl×n,H ∈ Rp×t,D ∈ Rl×t find X ∈ Rn×p such that Problem Ⅱ Given A ∈ Rm×...This paper, considers the following two problerns: Problem Ⅰ Given A ∈ Rm×n,B ∈ Rp×q,C ∈ Rm×q,G ∈ Rl×n,H ∈ Rp×t,D ∈ Rl×t find X ∈ Rn×p such that Problem Ⅱ Given A ∈ Rm×n,C ∈E Rm×m,G ∈ Rl×n,D ∈ Rl×l,find X ∈ SRn×n such that. Where ‖·‖ is Frobenius norm, SRn×n = {X ∈ Rn×n: X = XT} By applying the generalized singular value decompositions (GSVD) of matrix pairs,we obtain the general form of the solutions of Problem Ⅰ and Problem Ⅱ.展开更多
基金supported by the National Natural Science Foundation of China(1127105011371183+2 种基金61403036)the Science and Technology Development Foundation of CAEP(2013A04030202013B0403068)
文摘This paper, considers the following two problerns: Problem Ⅰ Given A ∈ Rm×n,B ∈ Rp×q,C ∈ Rm×q,G ∈ Rl×n,H ∈ Rp×t,D ∈ Rl×t find X ∈ Rn×p such that Problem Ⅱ Given A ∈ Rm×n,C ∈E Rm×m,G ∈ Rl×n,D ∈ Rl×l,find X ∈ SRn×n such that. Where ‖·‖ is Frobenius norm, SRn×n = {X ∈ Rn×n: X = XT} By applying the generalized singular value decompositions (GSVD) of matrix pairs,we obtain the general form of the solutions of Problem Ⅰ and Problem Ⅱ.
