| 酉对称矩阵的QR分解及其算法 |
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| 引用本文： | 蔺小林,蒋耀林. 酉对称矩阵的QR分解及其算法[J]. 计算机学报, 2005, 28(5): 817-822 |
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| 作者姓名： | 蔺小林 蒋耀林 |
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| 作者单位： | 西安交通大学理学院信息与系统科学研究所,西安,710049;陕西科技大学理学院,咸阳,712081;西安交通大学理学院信息与系统科学研究所,西安,710049 |
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| 基金项目： | 国家自然科学基金(10171080,60472003)，国家“八六三”高技术研究发展计划项目基金(2001AA111042)，陕西省教育厅专项基金(04JK204)资助.~~ |
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| 摘 要： | 该文讨论了酉对称矩阵QR分解中Q矩阵和R矩阵与母矩阵的Q矩阵和R矩阵之间的定量关系．从矩阵正交相抵的概念出发，给出了矩阵酉相抵的概念，证明了酉对称矩阵与母矩阵之间的酉相抵性，得到了酉相抵矩阵的Moore—Penrose逆等一些新的结论．同时，给出了酉对称矩阵的QR分解及其Moore—Penrose逆矩阵的算法．
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| 关 键 词： | 酉对称矩阵 QR分解 酉相抵 Moore-Penrose逆 并行算法 |
QR Decomposition and Algorithm for Unitary Symmetric Matrix |
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| LIN Xiao-lin,JIANG Yao-Lin. QR Decomposition and Algorithm for Unitary Symmetric Matrix[J]. Chinese Journal of Computers, 2005, 28(5): 817-822 |
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| Authors: | LIN Xiao-lin JIANG Yao-Lin |
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| Affiliation: | LIN Xiao-Lin~1),2) JIANG Yao-Lin~1) ~1) |
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| Abstract: | This paper discusses the quantitative correspondence of Q and R matrices of unitary symmetric matrices and its mother matrix. Based on definition of orthogonal counterbalance, authors definite the unitary counterbalance of matrix and prove the unitary counterbalance properties of unitary symmetric matrix and it's mother matrix, obtain some results as the Moore-Penrose inverses of unitary symmetric matrices are unitary counterbalance if unitary symmetric matrices are unitary counterbalance. At same time, authors give the algorithm of QR decomposition and Moore-Penrose inverses of unitary symmetric matrices. |
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| Keywords: | unitary symmetric matrix QR decomposition unitary counterbalance Moore-Penrose inverse parallel algorithms |
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