A Parallel Preconditioned Power Method for the Mazimum Eigenvalue of Real Symmetric Matrices

摘要：

This paper presents the preconditioned method for parallel solution to the maximum eigenvalue of real symmetric matrices by the power method. It is based on the low complexity information transmission of the banded matrix satisfying some bandwidth condition. We reduce the large-scale real symmetric dense matrix to a banded matrix by parallel Householder transformation, then solve the maximum eigenvalue of the banded matrix by the power method. Finally, some numerical experiments on Lenovo ShenTeng 1800 cluster are shown for the different bandwidth matrices formed by matrix transformation. Comparing it with the calculation results by the power method without pretreatment ,it is shown that if the bandwidth is the widest under a bandwidth condition our method has the highest parallel efficiency.

关键词： householder transform banded matriz power method

作者: Fangfang Cao Quanyi L(u) Yufeng Nie

作者单位: Department of Applied Mathematics, Northwest Polytechnical University, Xian, 710129

会议类型: 国际会议

会议名称: The Third International Workshop on Applied Matriz Theory(第三届国际矩阵分析与应用会议)

会议地点: 杭州

会议语种:英文

页码: 313-317

在线出版日期: 2009-07-09（万方平台首次上网日期，不代表论文的发表时间）