| 引用本文: | 仲妍,吴枫,骆志刚.一类典型结构矩阵的WZ分解.[J].国防科技大学学报,2010,32(4):157-164.[点击复制] |
| ZHONG Yan,WU Feng,LUO Zhigang.WZ Factorization for a Kind of Special Structured Matrix[J].Journal of National University of Defense Technology,2010,32(4):157-164[点击复制] |
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| 一类典型结构矩阵的WZ分解 |
| 仲妍, 吴枫, 骆志刚 |
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(国防科技大学 计算机学院，湖南 长沙410073)
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| 摘要: |
| WZ类矩阵分解是设计线性方程组求解中一类并行算法的数学理论基础。针对对称 p- 三对角矩阵，提出并证明该类典型结构矩阵的WZ分解式及其性质。进一步，当实对称 p- 三对角矩阵正定时，证明其WZ分解式中W因子具有元素均为实数的特点；当W因子对角线元素均为正实数时，分解式惟一。 |
| 关键词: 对称矩阵 p- 三对角矩阵 WZ分解 |
| DOI： |
| 投稿日期：2010-05-06 |
| 基金项目: |
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| WZ Factorization for a Kind of Special Structured Matrix |
| ZHONG Yan, WU Feng, LUO Zhigang |
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(College of Computer, National Univ. of Defense Technology, Changsha 410073, China)
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| Abstract: |
| The kind of WZ factorizations is the basic mathematics theory for a series of parallel algorithms in solving linear systems. For the symmetric p-tridiagonal matrix, the WZ factorization and its properties were proposed and proved. Furthermore, it also shows that the W-factor of the WZ factorization owns the character that the elements in itare real numbers when the real matrix is symmetric positive definite, and the factorization is unique when the elements in diagonal are positive real numbers. |
| Keywords: symmetric matrix p- tridiagonal matrix WZ factorization |
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