papers

Publications (21)

math.NA2018

Low synchronization GMRES algorithms

Kasia Swirydowicz, Julien Langou, Shreyas Ananthan +2

Communication-avoiding and pipelined variants of Krylov solvers are critical for the scalability of linear system solvers on future exascale architectures. We present low synchroni…

math.NA2025

Streaming Krylov-Accelerated Stochastic Gradient Descent

Stephen Thomas

We present SKA-SGD (Streaming Krylov-Accelerated Stochastic Gradient Descent), a novel optimization approach that accelerates convergence for ill-conditioned problems by projecting…

math.NA2023

ILU Smoothers for Low Mach Navier-Stokes Pressure Solvers

Stephen Thomas, Arielle Carr, Paul Mullowney +2

Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) -cycle for reducing high-frequency components of the error. However, the requisite direct triangular…

cs.CY2025

Thousands of AI Authors on the Future of AI

Katja Grace, Harlan Stewart, Julia Fabienne Sandkühler +4

In the largest survey of its kind, 2,778 researchers who had published in top-tier artificial intelligence (AI) venues gave predictions on the pace of AI progress and the nature an…

math.NA2021

Neumann Series in GMRES and Algebraic Multigrid Smoothers

Stephen Thomas, Arielle Carr, Paul Mullowney +2

Neumann series underlie both Krylov methods and algebraic multigrid smoothers. A low-synch modified Gram-Schmidt (MGS)-GMRES algorithm is described that employs a Neumann series to…

math.NA2023

Iterated Gauss-Seidel GMRES

Stephen Thomas, Erin Carson, Miro Rozložník +2

The GMRES algorithm of Saad and Schultz (1986) is an iterative method for approximately solving linear systems , with initial guess and residual ${\bf…