AF: Small: RUI: Toward High-Performance Block Krylov Subspace Algorithms for Solving Large-Scale Linear Systems

AF：小：RUI：用于求解大规模线性系统的高性能块 Krylov 子空间算法

• 批准号: 2327619
• 负责人: Hao Ji
• 金额: $ 60万
• 依托单位: Cal Poly Pomona Foundation, Inc.
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-10-01 至 2026-09-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2327619&HistoricalAwards=false
• 关键词: AF; Small; RUI; Toward; Performance

As data in the fields of science and engineering continues to grow in both size and complexity, existing numerical algorithms face challenges in efficiently handling large-scale linear algebra operations. The development of high-performance numerical algorithms has become crucial for enhancing the performance of data analysis and scientific computing applications on a large scale. This project aims to develop new numerical algorithms that effectively leverage the capabilities of high-performance computing to rapidly solve large-scale linear systems. This project will provide a valuable opportunity for students to engage in research and training activities at a primarily undergraduate institution focused on numerical methods and high-performance computing, which would greatly contribute to their career success in these fields. This project investigates the practical use of block Krylov subspace operations for the rapid solution of large-scale linear systems. Efficiency and cost-effectiveness are key considerations in optimizing block Krylov subspace algorithms. This project will explore appropriate matrix transformation techniques to design block Krylov subspace operations that are computationally efficient and effective. This project will also implement the block Krylov subspace operations for high-performance computing and evaluate their performance using various matrix data derived from real-life applications. The resulting block Krylov subspace algorithms developed in this project would greatly benefit domain experts in efficiently dealing with large-scale linear systems on high-performance computing platforms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

随着科学和工程领域的数据在规模和复杂性上继续增长，现有的数值算法在有效处理大规模线性代数操作方面面临着挑战。高性能数值算法的开发对于大规模增强数据分析和科学计算应用程序的性能至关重要。该项目旨在开发新的数值算法，以有效利用高性能计算的功能来快速求解大规模线性系统。该项目将为学生提供一个宝贵的机会，在主要的本科机构中，专注于数值方法和高性能计算，这将极大地促进他们在这些领域的职业成功。该项目研究了块Krylov子空间操作的实际使用，用于大规模线性系统的快速解决方案。效率和成本效益是优化Krylov子空间算法的关键考虑因素。该项目将探索适当的矩阵变换技术，以设计块krylov子空间操作，这些操作在计算上有效且有效。该项目还将实施块Krylov子空间操作，以进行高性能计算，并使用从现实生活应用程序中得出的各种矩阵数据来评估其性能。在该项目中开发的最终块Krylov子空间算法将极大地使领域专家有效地处理高性能计算平台上的大规模线性系统。该奖项反映了NSF的法定任务，并认为通过基金会的知识分子和更广泛的影响，可以通过评估来进行评估。