A fully parallel algorithm for the symmetric eigenvalue problem
A fully parallel algorithm for the symmetric eigenvalue problem
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DOI：
10.1137/0908018
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发表时间：
1985-11
影响因子：
3.7
通讯作者：
J. Dongarra;D. Sorensen
中科院分区：
文献类型：
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作者：
J. Dongarra;D. Sorensen
本文给出了对称代数特征值问题的一种并行算法。该算法基于Cuppen提出的计算对称三对角矩阵特征系统的分治方案。我们将这一思想扩展到一种并行算法，该算法在整个计算过程中保留了大于或等于初始数量的活动并行进程的数量。我们给出了一种新的压缩技术，它与鲁棒的寻根技术一起保证了特征系统在残差和特征向量正交性上的计算完全准确。简要分析了数值性质和对舍入误差的敏感性，以指出可能出现数值困难的地方。该算法能够在计算的所有级别上利用并行性，并且非常适合各种体系结构。给出了几种机器的计算结果。这些结果是非常令人鼓舞的，就…
In this paper we present a parallel algorithm for the symmetric algebraic eigenvalue problem. The algorithm is based upon a divide and conquer scheme suggested by Cuppen for computing the eigensystem of a symmetric tridiagonal matrix. We extend this idea to obtain a parallel algorithm that retains a number of active parallel processes that is greater than or equal to the initial number throughout the course of the computation. We give a new deflation technique which together with a robust root finding technique will assure computation of an eigensystem to full accuracy in the residuals and in the orthogonality of eigenvectors. A brief analysis of the numerical properties and sensitivity to round off error is presented to indicate where numerical difficulties may occur. The algorithm is able to exploit parallelism at all levels of the computation and is well suited to a variety of architectures.Computational results are presented for several machines. These results are very encouraging with respect to both...