| 引用本文: | 吴建平,李晓梅.块三对角矩阵的修正型局部块分解预条件.[J].国防科技大学学报,2002,24(2):73-76 ,100.[点击复制] |
| WU Jianping,LI Xiaomei.Modified Preconditioners to Block Tridiagonal Matrices Based on Local Factorization[J].Journal of National University of Defense Technology,2002,24(2):73-76 ,100[点击复制] |
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| 块三对角矩阵的修正型局部块分解预条件 |
| 吴建平1, 李晓梅2 |
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(1.国防科技大学 计算机学院，湖南 长沙 410073;2.指挥技术学院，北京 101416)
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| 摘要: |
| 利用块三对角阵分解因子构造了一类修正型不完全分解预条件子，分析了该预条件子的存在性及其若干性质。针对从二维Laplace算子离散得到的五点差分矩阵，给出了预条件后的实际条件数，结果表明，条件数与矩阵阶数的平方根成正比，并且比例因子随局部分解步长的增大而逐渐减小。具体实现时，考虑了其高效实现方案，并针对从二维Laplace算子与系数不连续的二维椭圆型算子离散得到的五点差分矩阵，在主频为550MHz，内存为256MB的微机上作了大量实验，且与其他较有效的预条件方法进行了比较，结果表明该预条件方法效率优于其他测试预条件。 |
| 关键词: 对称正定矩阵 不完全分解 预条件子 |
| DOI： |
| 投稿日期：2001-10-08 |
| 基金项目: |
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| Modified Preconditioners to Block Tridiagonal Matrices Based on Local Factorization |
| WU Jianping1, LI Xiaomei2 |
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(1.College of Computer, National Univ. of Defense Technology, Changsha 410073, China;2.Institute of Command and Technology, Beijing 101416，China)
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| Abstract: |
| A modified type of preconditioner is constructed with the help of local block factorization of block tridiagonal matrices. Then the existence and the properties are analyzed. For the standard 5-point matrices, which are derived from the 2-D Laplace operator, the actual condition numbers of the preconditioned matrices are computed. The result shows that the condition number is proportioned to the square root of the order of the matrix. What's more, the longer the step of the local factorization, the smaller the coefficient is. Then efficient implementations of the preconditioners are focused on and three of them provided. Finally lots of experiments are performed for the constructed preconditioners and the well-known effective ones on the personal computer with main frequency of 550MHz and memory of 256M. The matrices in these experiments include the standard five point ones, and the ones derived from a 2-D elliptic operator with discontinuous coefficients. The results also show that the preconditioners are more efficient than the other tested ones. |
| Keywords: symmetric positive definite matrix incomplete factorization preconditioner |
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