Investigating the Benefit of FP16-Enabled Mixed-Precision Solvers for Symmetric Positive Definite Matrices Using GPUs

Ahmad Abdelfattah, Stan Tomov, Jack Dongarra

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Half-precision computation refers to performing floating-point operations in a 16-bit format. While half-precision has been driven largely by machine learning applications, recent algorithmic advances in numerical linear algebra have discovered beneficial use cases for half precision in accelerating the solution of linear systems of equations at higher precisions. In this paper, we present a high-performance, mixed-precision linear solver ( 퐴푥=푏 ) for symmetric positive definite systems in double-precision using graphics processing units (GPUs). The solver is based on a mixed-precision Cholesky factorization that utilizes the high-performance tensor core units in CUDA-enabled GPUs. Since the Cholesky factors are affected by the low precision, an iterative refinement (IR) solver is required to recover the solution back to double-precision accuracy. Two different types of IR solvers are discussed on a wide range of test matrices. A preprocessing step is also developed, which scales and shifts the matrix, if necessary, in order to preserve its positive-definiteness in lower precisions. Our experiments on the V100 GPU show that performance speedups are up to 4.7 × against a direct double-precision solver. However, matrix properties such as the condition number and the eigenvalue distribution can affect the convergence rate, which would consequently affect the overall performance.
Original languageEnglish
Title of host publicationComputational Science – ICCS 2020
Pages237-250
DOIs
Publication statusE-pub ahead of print - 15 Jun 2020

Publication series

NameComputational Science – ICCS 2020
Volume12138
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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