2025/07/23 by Vasileios Kalantzis, Kalantzis, Vasileios, Mark S. Squillante +3
Computer Science · Mathematics · #65F22 #Advanced Optimization Algorithms Research #Data Structures and Algorithms (cs.DS) #F.2.1 #FOS: Computer and information sciences #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2507.17673
openalex publication_date 2025/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Iterative solvers for large-scale linear systems such as Krylov subspace methods can diverge when the linear system is ill-conditioned, thus significantly reducing the applicability of these iterative methods in practice for high-performance computing solutions of such large-scale linear systems. To address this fundamental problem, we propose general algorithmic frameworks to modify Krylov subspace iterative solution methods which ensure that the algorithms are stable and do not diverge. We then apply our general frameworks to current implementations of the corresponding iterative methods in SciPy and demonstrate the efficacy of our stable iterative approach with respect to numerical experiments across a wide range of synthetic and real-world ill-conditioned linear systems.