Random sketching to enhance the numerical stability of block orthogonalization algorithms for s-step GMRES

IF 1.1 4区计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Parallel Computing Pub Date : 2026-06-01 Epub Date: 2026-05-22 DOI:10.1016/j.parco.2026.103197

Ichitaro Yamazaki , Andrew J. Higgins , Erik G. Boman , Daniel B. Szyld

引用次数: 0

Abstract

We integrate random sketching techniques into block orthogonalization schemes needed for

s

-step GMRES. The resulting, one-stage and two-stage, block orthogonalization schemes generate the basis vectors whose overall orthogonality error is bounded by machine precision as long as each of the corresponding block vectors are numerically full rank. We implement these randomized block orthogonalization schemes using standard distributed-memory linear algebra kernels for

s

-step GMRES available in the Trilinos software packages. Our performance results on the Perlmutter supercomputer (with four NVIDIA A100 GPUs per node) demonstrate that these randomized techniques can enhance the numerical stability of the orthogonalization and overall solver, without a significant increase in the execution time.

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随机绘制提高s步GMRES分块正交化算法数值稳定性

我们将随机素描技术整合到s步GMRES所需的块正交化方案中。所得到的一阶段和两阶段块正交化方案产生的基向量，只要每个相应的块向量在数值上是满秩的，其总体正交性误差就以机器精度为界。我们使用Trilinos软件包中提供的s步GMRES的标准分布式内存线性代数内核来实现这些随机块正交化方案。我们在Perlmutter超级计算机（每个节点有四个NVIDIA A100 gpu）上的性能结果表明，这些随机化技术可以增强正交化和整体求解器的数值稳定性，而不会显著增加执行时间。

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