Best approximate solution of matrix equation AXB+CY D=E
文献类型：期刊论文
| 作者 | Liao, AP; Bai, ZZ ; Lei, Y
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| 刊名 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
 |
| 出版日期 | 2005 |
| 卷号 | 27期号:3页码:675-688 |
| 关键词 | matrix equation least-squares solution best approximate solution generalized singular value decomposition canonical correlation decomposition |
| ISSN号 | 0895-4798 |
| DOI | 10.1137/040615791 |
| 英文摘要 | We derive an analytical expression of the best approximate solution in the least-squares solution set SE of the matrix equation AXB + CYD = E to a given matrix pair (X-f, Y-f), where A, B, C, D, and E are given matrices of suitable sizes. Our work is based on the projection theorem in the finite-dimensional inner product space, and we use the generalized singular value decomposition and the canonical correlation decomposition. Moreover, we establish a direct method for computing this best approximate solution. An algorithm for finding the best approximate solution is described in detail, and an example is used to show the feasibility and effectiveness of our algorithm. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000236098800006 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/1330]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Liao, AP |
| 作者单位 | 1.Hunan Univ, Coll Math & Economet, Changsha 410082, Peoples R China 2.Fudan Univ, Dept Math, Shanghai 200433, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Liao, AP,Bai, ZZ,Lei, Y. Best approximate solution of matrix equation AXB+CY D=E[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2005,27(3):675-688. |
| APA | Liao, AP,Bai, ZZ,&Lei, Y.(2005).Best approximate solution of matrix equation AXB+CY D=E.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,27(3),675-688. |
| MLA | Liao, AP,et al."Best approximate solution of matrix equation AXB+CY D=E".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 27.3(2005):675-688. |
入库方式： OAI收割
来源：数学与系统科学研究院
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