scholarly journals GPU-Accelerated Asynchronous Error Correction for Mixed Precision Iterative Refinement

2012 ◽  
pp. 908-919 ◽  
Author(s):  
Hartwig Anzt ◽  
Piotr Luszczek ◽  
Jack Dongarra ◽  
Vincent Heuveline
Keyword(s):  
Error Correction ◽  
Iterative Refinement ◽  
Mixed Precision

scholarly journals GPU-Accelerated Asynchronous Error Correction for Mixed Precision Iterative Refinement

2011 ◽  
Author(s):  
Hartwig Antz ◽  
Piotr Luszczek ◽  
Jack Dongarra ◽  
Vinent Heuveline
Keyword(s):  
Error Correction ◽  
Iterative Refinement ◽  
Mixed Precision

Residual Replacement in Mixed-Precision Iterative Refinement for Sparse Linear Systems

2018 ◽  
pp. 554-561
Author(s):  
Hartwig Anzt ◽  
Goran Flegar ◽  
Vedran Novaković ◽  
Enrique S. Quintana-Ortí ◽  
Andrés E. Tomás
Keyword(s):  
Linear Systems ◽  
Iterative Refinement ◽  
Sparse Linear Systems ◽  
Mixed Precision

scholarly journals Mixed Precision Iterative Refinement Techniques for the Solution of Dense Linear Systems

2007 ◽  
Vol 21 (4) ◽  
pp. 457-466 ◽  
Author(s):  
Alfredo Buttari ◽  
Jack Dongarra ◽  
Julie Langou ◽  
Julien Langou ◽  
Piotr Luszczek ◽  
...  
Keyword(s):  
Linear Systems ◽  
Iterative Refinement ◽  
Mixed Precision

scholarly journals Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200110
Author(s):  
Azzam Haidar ◽  
Harun Bayraktar ◽  
Stanimire Tomov ◽  
Jack Dongarra ◽  
Nicholas J. Higham
Keyword(s):  
Linear Systems ◽  
Numerical Stability ◽  
High Performance ◽  
Iterative Refinement ◽  
Floating Point ◽  
Double Precision ◽  
Floating Point Arithmetic ◽  
Mixed Precision ◽  
Scientific Simulations ◽  
Point Arithmetic

Double-precision floating-point arithmetic (FP64) has been the de facto standard for engineering and scientific simulations for several decades. Problem complexity and the sheer volume of data coming from various instruments and sensors motivate researchers to mix and match various approaches to optimize compute resources, including different levels of floating-point precision. In recent years, machine learning has motivated hardware support for half-precision floating-point arithmetic. A primary challenge in high-performance computing is to leverage reduced-precision and mixed-precision hardware. We show how the FP16/FP32 Tensor Cores on NVIDIA GPUs can be exploited to accelerate the solution of linear systems of equations Ax  =  b without sacrificing numerical stability. The techniques we employ include multiprecision LU factorization, the preconditioned generalized minimal residual algorithm (GMRES), and scaling and auto-adaptive rounding to avoid overflow. We also show how to efficiently handle systems with multiple right-hand sides. On the NVIDIA Quadro GV100 (Volta) GPU, we achieve a 4 × − 5 × performance increase and 5× better energy efficiency versus the standard FP64 implementation while maintaining an FP64 level of numerical stability.

scholarly journals On Mixed Precision Iterative Refinement for Eigenvalue Problems

2013 ◽  
Vol 18 ◽  
pp. 2647-2650 ◽  
Author(s):  
Karl E. Prikopa ◽  
Wilfried N. Gansterer
Keyword(s):  
Eigenvalue Problems ◽  
Iterative Refinement ◽  
Mixed Precision

Forced choice error correction with ambiguous error feedback

2009 ◽  
Author(s):  
Elena G. Patsenko ◽  
Erik M. Altmann
Keyword(s):  
Error Correction ◽  
Forced Choice ◽  
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