| ON SOLUTIONS OF MATRIX EQUATION AXAT ＋ BYBT=C |
| |
| 作者姓名： | Yuan-beiDeng Xi-yanHu |
| |
| 作者单位： | [1]ICMSEC,AcademyofMathematicsandSystemSciences,ChineseAcademyofSciences,Beijing100080,China [2]CollegeofMathematicsandEconometrics,HunanUniversity,Changsha310082,China |
| |
| 基金项目： | Supported by the NNSF of China. |
| |
| 摘 要： | By making use of the quotient singular value decomposition (QSVD) of a matrix pair,this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the general solutions of the linear matrix equation AXA^T BYB^T=C with the unknown X and Y, which may be both symmetric, skew-symmetric, nonnegativede finite, positive definite or some cross combinations respectively. Also, the solutions of some optimal problems are derived.
|
| 关 键 词： | 矩阵范数 矩阵方程 QSVD 约束条件 最优化问题 |
ON SOLUTIONS OF MATRIX EQUATION AXA~T+BYB~T=C |
| |
| Yuan-beiDeng Xi-yanHu.ON SOLUTIONS OF MATRIX EQUATION AXA~T+BYB~T=C[J].Journal of Computational Mathematics,2005,23(1):17-26. |
| |
| Authors: | Yuan-bei Deng |
| |
| Abstract: | By making use of the quotient singular value decomposition(QSVD)of a matrix pair,this paper establishes the necessary and sufficient conditions for the existence of and theexpressions for the general solutions of the linear matrix equation AXA~T+BYB~T=Cwith the unknown X and Y,which may be both symmetric,skew-symmetric,nonnegativedefinite,positive definite or some cross combinations respectively.Also,the solutions ofsome optimal problems are derived. |
| |
| Keywords: | Matrix equation Matrix norm QSVD Constrained condition Optimal problem |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
