7 papers
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…
Mixed precision solvers for the all-at-once Runge--Kutta discretization of the heat equation
Santolo Leveque, Luca Bergamaschi, Ángeles Martínez +1
We study the effect of mixed precision on the numerical integration of the heat equation discretized with a Runge--Kutta method in time. A full space-time discretization is applied…
Balancing Inexactness in Mixed Precision Matrix Computations
Erin Claire Carson
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspe…
Mixed precision multigrid with smoothing based on incomplete Cholesky factorization
Petr Vacek, Hartwig Anzt, Erin Carson +3
Multigrid methods are popular iterative methods for solving large-scale sparse systems of linear equations. We present a mixed precision formulation of the multigrid V-cycle method…
Mixed precision sketching for least-squares problems and its application in GMRES-based iterative refinement
Erin Carson, Ieva Daužickaitė
Sketching-based preconditioners have been shown to accelerate the solution of dense least-squares problems with coefficient matrices having substantially more rows than columns. Th…
The Detection and Correction of Silent Errors in Pipelined Krylov Subspace Methods
Erin Claire Carson, Jakub Hercík
As computational machines become larger and more complex, the probability of hardware failure rises. ``Silent errors'', or bit flips, may not be immediately apparent but can cause…
A comparison of mixed precision iterative refinement approaches for least-squares problems
Erin Carson, Ieva Daužickaitė
Various approaches to iterative refinement (IR) for least-squares problems have been proposed in the literature and it may not be clear which approach is suitable for a given probl…