两类矩阵方程的极小范数解  

THE MINIMUM NORM SOLUTIONS OF TWO CLASSES OF MATRIX EQUATIONS

作　　者：袁永新[1] 

机构地区：[1]华东船舶工业学院基础学科系,镇江212003

出　　处：《高等学校计算数学学报》2002年第2期127-134,共8页Numerical Mathematics A Journal of Chinese Universities

摘　　要：1.引言 设Rm×n表示所有m×n阶实矩阵的集合,SRn×n是所有n阶实对称矩阵的全体,ORn×n为n阶实正交矩阵的全体,Ix是n阶单位矩阵,AT、rankA分别表示矩阵A的转置与秩,‖·‖是矩阵的Frobenius范数.In this paper, the following problems are considered:Problem Ⅰ Given A∈Rm×n,B∈Rp×n ,C∈Rn×n. Let S1= {X:X∈Rm×p, ATXB+BTXTA=C}. Find X∈Sl such that || X || =min.Problem Ⅱ Given A∈Rm×n,B∈m×p,C∈Rp×p,D∈Rp×p. Let S2={X:X∈sR=m×m,ATXA=C,BTXB=D}. Find X=S2 such that || X || =min.By applying the generalized singular-value and canonical correlation decompositions of matrix pairs, the necessary and sufficient conditions, under which S2 and S2 are nonempty, are studied. The expressions for the solutions of Problems Ⅰ and Ⅱ are given.

关 键 词：矩阵方程 极小范数解 相容性条件 相容方程 

分 类 号：O241.6[理学—计算数学]