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

随着科学和工程领域中的数据在规模和复杂性方面持续增长，现有的数值算法在有效处理大规模线性代数运算方面面临挑战。高性能数值算法的开发对于大规模提高数据分析和科学计算应用的性能至关重要。该项目旨在开发新的数值算法，有效地利用高性能计算的能力来快速解决大规模线性系统。该项目将为学生提供一个宝贵的机会，让他们在一个主要侧重于数值方法和高性能计算的本科院校从事研究和培训活动，这将大大有助于他们在这些领域的职业成功。本计画探讨区块Krylov子空间运算在大规模线性系统快速求解中的实际应用。效率和成本效益是优化块Krylov子空间算法的关键考虑因素。这个项目将探讨适当的矩阵变换技术来设计块Krylov子空间运算，计算效率和有效的。该项目还将实现用于高性能计算的块Krylov子空间运算，并使用来自实际应用的各种矩阵数据评估其性能。在这个项目中开发的块Krylov子空间算法将极大地有利于领域专家在高性能计算平台上有效地处理大规模线性系统。这个奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.