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| 求解带状线性方程组的一种并行算法 | |
| 引用本文： | 段治健,杨永,马欣荣,刘三阳.求解带状线性方程组的一种并行算法[J].计算机科学,2010,37(3):242-244270. |
| 作者姓名： | 段治健 杨永 马欣荣 刘三阳 |
| 作者单位： | 1. 西北工业大学翼型叶栅空气动力学国防科技重点实验室,西安,710072 2. 西安电子科技大学理学院应用数学系,西安,710071;咸阳师范学院数学与信息科学学院,咸阳,712000 3. 西安电子科技大学理学院应用数学系,西安,710071 |
| 基金项目： | 咸阳师范学院重点建设课程项目基金(No.200812014)资助 |
| 摘 要： | 提出了一种在MIMD分布式存储环境下求解带状线性方程组的交替方向迭代并行算法。利用系数矩阵的结构特点分裂矩阵,使整个计算过程只在相邻处理机间通信两次。给出了系数矩阵分别为Hermite正定矩阵和M-矩阵时算法收敛的充分条件。最后,在HP rx2600集群系统上进行的数值计算表明,该算法与多分裂方法相比具有较高的加速比和并行效率。 |
| 关 键 词： | 带状线性方程组 交替方向迭代 HP rx2600集群 并行性 |
| 收稿时间： | 4/9/2009 12:00:00 AM |
| 修稿时间： | 2009/6/22 0:00:00 |
Parallel Algorithm for Solving Banded Linear Systems |
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| DUAN Zhi-jian,YANG Yong,MA Xin-rong,LIU San-yang.Parallel Algorithm for Solving Banded Linear Systems[J].Computer Science,2010,37(3):242-244270. | |
| Authors: | DUAN Zhi-jian YANG Yong MA Xin-rong LIU San-yang |
| Affiliation: | (National Key Laboratory of Aerodynamic Design and Research, Northwestern Polytechnical University, Xi' an 710072 ,China);(Department of llpplied Mathematics,Xidian University,Xi'an 710071,China);(Department of Mathematics,Xianyang Normal University,Xianyang 712000,China) |
| Abstract: | The work presented in this paper focused on alternating-direction parallel iterative method for solving banded-linear systems on distributed-memory multi-computers.Firstly,the matrix was splitted by using the feature of the coefficient matrix,thus the communication only need twice between the adjacent processors per iteration step.Furthermore,the sufficient conditions for convergence were given when the coefficient matrix A is a Hermite positive definite matrix or M-matrix respectively.Finally,the numerical... |
| Keywords: | Banded linear systems Alternating-direction iteration HP rx2600 cluster Parallelism |
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