| 关于酉对称矩阵的QR分解及其算法 |
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| 引用本文： | 袁晖坪. 关于酉对称矩阵的QR分解及其算法[J]. 系统科学与数学, 2012, 32(2): 172-180 |
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| 作者姓名： | 袁晖坪 |
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| 作者单位： | 重庆工商大学电子商务及供应链系统重庆市重点实验室,重庆400067;重庆工商大学数学与统计学院,重庆400067 |
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| 基金项目： | 国家自然科学基金(10871217)重庆市自然科学基金(CSTS2005BB0243)资助课题 |
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| 摘 要： | 为了简化大型行(列)酉对称矩阵的QR分解,研究了行(列)酉对称矩阵的性质,获得了一些新的结果,给出了行(列)酉对称矩阵的QR分解的公式和快速算法,它们可极大地减少行(列)酉对称矩阵的QR分解的计算量与存储量,并且不会丧失数值精度.同时推广和丰富了邹红星等(2002)的研究内容,拓宽了实际应用领域的范围.
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| 关 键 词： | 行(列)对称矩阵 行(列)酉对称矩阵 QR分解 并行算法 |
ON QR FACTORIZATION AND ALGORITHM FOR UNITARY SYMMETRIC MATRIX |
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| YUAN Huiping. ON QR FACTORIZATION AND ALGORITHM FOR UNITARY SYMMETRIC MATRIX[J]. Journal of Systems Science and Mathematical Sciences, 2012, 32(2): 172-180 |
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| Authors: | YUAN Huiping |
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| Affiliation: | YUAN Huiping (Chongqing Key Laboratory of Electronic Commerce & Supply Chain System,Chongqing Technology and Business University,Chongqing 400067;College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067) |
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| Abstract: | To simplify the QR factorization of row(column)unitary symmetric large matrix, the properties of row(column)unitary symmetric matrix are studied,and some new results are gained.The formula and fast algorithm method for the QR factorization of row(column) unitary symmetric matrix are obtained,those formula could reduce the amount of calculation for QR factorization of row(column)unitary symmetric matrix greatly,save dramatically the CPU time and memory without loss of any numerical precision.Some results of Zou,et al. (2002)are generalized. |
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| Keywords: | Row(column)symmetric matrix row(column)unitary symmetric matrix QR factorization parallel algorithms |
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