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

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type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
title	Investigating the Benefit of FP16-Enabled Mixed-Precision Solvers for Symmetric Positive Definite Matrices Using GPUs
Creator	Dongarra, Jack Abdelfattah, Ahmad Tomov, Stan
topic	covid:71706fffc479f9e381ae2c0467b0a33b5f93eb94#this
source	PMC
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 ([Formula: see text]) 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[Formula: see text] 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.
has issue date	2020-06-15(xsd:dateTime)
bibo:doi	10.1007/978-3-030-50417-5_18
has license	no-cc
sha1sum (hex)	71706fffc479f9e381ae2c0467b0a33b5f93eb94
schema:url	https://doi.org/10.1007/978-3-030-50417-5_18
resource representing a document's title	Investigating the Benefit of FP16-Enabled Mixed-Precision Solvers for Symmetric Positive Definite Matrices Using GPUs
has PubMed Central identifier	PMC7302814
schema:publication	Computational Science - ICCS 2020
resource representing a document's body	covid:71706fffc479f9e381ae2c0467b0a33b5f93eb94#body_text
is http://vocab.deri.ie/void#inDataset of	https://covidontheweb.inria.fr:4443/about/id/http/ns.inria.fr/covid19/71706fffc479f9e381ae2c0467b0a33b5f93eb94
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