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

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.