Publications (21)
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…
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…
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…
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…
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…
Iterated Gauss-Seidel GMRES
Stephen Thomas, Erin Carson, Miro RozložnÃk +2
The GMRES algorithm of Saad and Schultz (1986) is an iterative method for approximately solving linear systems , with initial guess and residual ${\bf…