Improved parallel Arnoldi method for solving linear equations

doi:10.3778/j.issn.1002-8331.2009.22.014

Computer Engineering and Applications ›› 2009, Vol. 45 ›› Issue (22): 41-43.DOI: 10.3778/j.issn.1002-8331.2009.22.014

• 研究、探讨 • Previous Articles Next Articles

Improved parallel Arnoldi method for solving linear equations

WANG Bao ^1，2，LV Quan-yi¹，FAN Yan-hong¹，NIE Yu-feng¹

1.Department of Applied Mathematics，Northwestern Polytechnical University，Xi’an 710072，China
2.Academy of Aeronautics，Northwestern Polytechnical University，Xi’an 710072，China

Received:2008-04-28 Revised:2008-07-21 Online:2009-08-01 Published:2009-08-01
Contact: WANG Bao

改进的求解线性方程组的并行Arnoldi方法

汪保^1，2，吕全义¹，樊艳红¹，聂玉峰¹

1.西北工业大学应用数学系，西安 710072
2.西北工业大学航空学院，西安 710072

通讯作者: 汪保

Abstract

Abstract: A parallel algorithm based on Galerkin method for cycle block-tridiagonal linear equations on distributed-memory multi-computers is presented.A group of vectors spanning subspace chosen properly，the algorithm is no disrupted.In theory，convergence is proved when the coefficient matrix A is a symmetric positive definite matrix.Finally，some numerical results on HP rx2600 cluster show that practice computing is consistent with theory.

Key words: cycle block-tridiagonal linear equations, parallel algorithm, Arnoldi method

摘要： 以Galerkin原理为基础，提出了求解循环块三对角线性方程组的并行算法。根据系数矩阵的稀疏性，选取适当的子空间的基，使算法不但不会发生中断，并从理论上证明了当系数矩阵对称正定时，该并行算法收敛。最后，在HP rx2600集群上进行的数值实验结果表明，该算法的并行效率很高，理论和实际计算相一致。

关键词: 循环块三对角线性方程组, 并行算法, Arnoldi方法

WANG Bao ^1，2，LV Quan-yi¹，FAN Yan-hong¹，NIE Yu-feng¹. Improved parallel Arnoldi method for solving linear equations[J]. Computer Engineering and Applications, 2009, 45(22): 41-43.

汪保^1，2，吕全义¹，樊艳红¹，聂玉峰¹. 改进的求解线性方程组的并行Arnoldi方法
[J]. 计算机工程与应用, 2009, 45(22): 41-43.

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Improved parallel Arnoldi method for solving linear equations

改进的求解线性方程组的并行Arnoldi方法

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