| 行(列)对称矩阵的LDU分解与Cholesky分解 |
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| 引用本文： | 袁晖坪. 行(列)对称矩阵的LDU分解与Cholesky分解[J]. 华侨大学学报(自然科学版), 2007, 28(1): 88-91 |
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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,理学院,重庆,400067 |
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| 基金项目： | 重庆市自然科学基金资助项目(CSTS2005BB0243)，重庆市教委科研基金资助项目(3-10-71) |
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| 摘 要： | 提出行(列)转置矩阵与行(列)对称矩阵的概念,研究它们的性质,获得一些新的结果.给出行(列)对称矩阵的LDU分解、Cholesky分解和三对角分解公式,可极大地减少行(列)对称矩阵的LDU分解、Cholesky分解和三对角分解的计算量与存储量,而且不会丧失数值精度.
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| 关 键 词： | 行(列)转置矩阵 行(列)对称矩阵 LDU分解 Cholesky分解 三对角分解 |
| 文章编号： | 1000-5013（2007）01-0088-04 |
| 修稿时间： | 2006-05-15 |
LDU Factorization and Cholesky Factorization of Row (Column) Symmetric Matrices |
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| YUAN Hui-ping. LDU Factorization and Cholesky Factorization of Row (Column) Symmetric Matrices[J]. Journal of Huaqiao University(Natural Science), 2007, 28(1): 88-91 |
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| Authors: | YUAN Hui-ping |
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| Affiliation: | School of Science, Chongqing Technology and Business University, Chongqing 400067, China |
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| Abstract: | The concept of row(column) transposed matrix and row(column) symmetric matrix are defined.Their basic properties are studied and some new results are obtained.The formula for the LDU factorization,Cholesky factorization and triple diagonal factorization of row(column) symmetric matrix are obtained.These formula can dramatically reduce the amount of calculation for LDU factorization,Cholesky factorization and triple diagonal factorization of row(column) symmetric matrix,save dramatically the CPU time and memory without loss of any numerical precision. |
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| Keywords: | row(column) transposed matrix row(column) symmetric matrix LDU factorization Cholesky factorization triple diagonal factorization |
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