Efficient parallel reduction of bandwidth for symmetric matrices

IF 2 4区计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Parallel Computing Pub Date : 2023-02-01 DOI:10.1016/j.parco.2023.102998

Valeriy Manin, Bruno Lang

引用次数: 0

Abstract

Bandwidth reduction can be a first step in the computation of eigenvalues and eigenvectors for a wide-banded complex Hermitian (or real symmetric) matrix. We present algorithms for this reduction and the corresponding back-transformation of the eigenvectors. These algorithms rely on blocked Householder transformations, thus enabling level 3 BLAS performance, and they feature two levels of parallelism. The efficiency of our approach is demonstrated with numerical experiments.

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有效的并行减少带宽对称矩阵

带宽缩减可以是计算宽带复埃尔米特（或实对称）矩阵的特征值和特征向量的第一步。我们提出了这种约简的算法和相应的特征向量的反变换。这些算法依赖于阻塞的Householder转换，从而实现了级别3的BLAS性能，并且具有两个级别的并行性。数值实验证明了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Parallel Computing 工程技术-计算机：理论方法

CiteScore

3.50

自引率

7.10%

发文量

审稿时长

4.5 months

期刊介绍： Parallel Computing is an international journal presenting the practical use of parallel computer systems, including high performance architecture, system software, programming systems and tools, and applications. Within this context the journal covers all aspects of high-end parallel computing from single homogeneous or heterogenous computing nodes to large-scale multi-node systems. Parallel Computing features original research work and review articles as well as novel or illustrative accounts of application experience with (and techniques for) the use of parallel computers. We also welcome studies reproducing prior publications that either confirm or disprove prior published results. Particular technical areas of interest include, but are not limited to: -System software for parallel computer systems including programming languages (new languages as well as compilation techniques), operating systems (including middleware), and resource management (scheduling and load-balancing). -Enabling software including debuggers, performance tools, and system and numeric libraries. -General hardware (architecture) concepts, new technologies enabling the realization of such new concepts, and details of commercially available systems -Software engineering and productivity as it relates to parallel computing -Applications (including scientific computing, deep learning, machine learning) or tool case studies demonstrating novel ways to achieve parallelism -Performance measurement results on state-of-the-art systems -Approaches to effectively utilize large-scale parallel computing including new algorithms or algorithm analysis with demonstrated relevance to real applications using existing or next generation parallel computer architectures. -Parallel I/O systems both hardware and software -Networking technology for support of high-speed computing demonstrating the impact of high-speed computation on parallel applications