206 citations · 805 across the 35 of their papers we have counts for
21 papers · 1 filter
Mixed-Precision Computing for Scientific Discovery: Formats, Co-Design, and Responsible Approximation
Emmanuel Agullo, Hartwig Anzt, Daniel Bauer +37
Reduced and mixed precision have moved from a niche optimization to a central design axis in scientific computing and engineering, driven by energy constraints, heterogeneous accel…
How to grade the accuracy of the BLAS
James Demmel, Greg Henry, Igor Kozachenko +4
Motivated by accelerating machine learning (ML), many computer vendors and chip manufacturers are building accelerators for matrix multiplication, which save time and energy by ope…
Numerical analysis of Givens rotation
Weslley da Silva Pereira, Ali Lotfi, Julien Langou
Generating 2-by-2 unitary matrices in floating-precision arithmetic is a delicate task. One way to reduce the accumulation error is to use less floating-point operations to compute…
A new deflation criterion for the QZ algorithm
Thijs Steel, Raf Vandebril, Julien Langou
The QZ algorithm computes the Schur form of a matrix pencil. It is an iterative algorithm and at some point, it must decide that an eigenvalue has converged and move on with anothe…
Low-Synch Gram-Schmidt with Delayed Reorthogonalization for Krylov Solvers
Daniel Bielich, Julien Langou, Stephen Thomas +3
The parallel strong-scaling of Krylov iterative methods is largely determined by the number of global reductions required at each iteration. The GMRES and Krylov-Schur algorithms e…
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…