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Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores

Journal Article · · SIAM Journal on Scientific Computing
DOI:https://doi.org/10.1137/21m1465032· OSTI ID:2424939
 [1];  [2];  [3];  [4];  [2]
  1. Department of Computer Science, Upper Mountjoy Campus, Durham University, Durham DH1 3LE, UK.
  2. Department of Mathematics, University of Manchester, Manchester M13 9PL, UK.
  3. Livermore Software Technology, ANSYS Company, Livermore, CA 94551 USA.
  4. Sorbonne Université, CNRS, LIP6, Paris 75005, France.
+ Show Author Affiliations

Not provided.

Research Organization:
US Department of Energy (USDOE), Washington, DC (United States). Office of Science, Exascale Computing Project
Sponsoring Organization:
USDOE
OSTI ID:
2424939
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 1 Vol. 45; ISSN 1064-8275
Publisher:
Society for Industrial and Applied Mathematics (SIAM)
Country of Publication:
United States
Language:
English

References (12)

Stochastic rounding: implementation, error analysis and applications journal March 2022
Accuracy and Stability of Numerical Algorithms book January 2002
Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels with Random Data journal January 2020
Performance and energy consumption of accurate and mixed-precision linear algebra kernels on GPUs journal July 2020
Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems journal January 2019
Stochastic Rounding and Its Probabilistic Backward Error Analysis journal January 2021
A New Approach to Probabilistic Rounding Error Analysis journal January 2019
Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Cores journal January 2020
A Class of Fast and Accurate Summation Algorithms journal January 2020
Numerical behavior of NVIDIA tensor cores journal January 2021
A survey of numerical linear algebra methods utilizing mixed-precision arithmetic journal March 2021
Mixed precision algorithms in numerical linear algebra journal May 2022

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Related Subjects

Mathematics