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Title: Parallel conjugate gradient: effects of ordering strategies, programming paradigms, and architectural platforms

Abstract

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. A sparse matrix-vector multiply (SPMV) usually accounts for most of the floating-point operations with a CG iteration. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and SPMV using different programming and architectures. Results show that for this class of applications, ordering significantly improves overall performance, that cache reuse may be more important than reducing communication, and that it is possible to achieve message passing performance using shared memory constructs through careful data ordering and distribution. However, a multithreaded implementation of CG on the Tera MTA does not require special ordering or partitioning to obtain high efficiency and scalability.

Authors:
; ; ;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab., CA (US)
Sponsoring Org.:
USDOE Director, Office of Science. Office of Advanced Scientific Computing Research. Mathematical, Information, and Computational Sciences Division; National Aeronautics and Space Administration (US)
OSTI Identifier:
775130
Report Number(s):
LBNL-45828
R&D Project: 618310; TRN: AH200110%%117
DOE Contract Number:  
AC03-76SF00098
Resource Type:
Conference
Resource Relation:
Conference: 13th International Conference on Parallel and Distributed Computing Systems, Las Vegas, NV (US), 08/08/2000--08/10/2000; Other Information: PBD: 1 May 2000
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; COMPUTER ARCHITECTURE; ALGORITHMS; ITERATIVE METHODS; EFFICIENCY; IMPLEMENTATION; PERFORMANCE; PARALLEL PROCESSING; ORDERING ALGORITHMS UNSTRUCTURED MESHES SPARSE MATRICES DISTRIBUTED AND SHARED MEMORY MULTITHREADING

Citation Formats

Oliker, L., Li, X., Heber, G., and Biswas, R. Parallel conjugate gradient: effects of ordering strategies, programming paradigms, and architectural platforms. United States: N. p., 2000. Web.
Oliker, L., Li, X., Heber, G., & Biswas, R. Parallel conjugate gradient: effects of ordering strategies, programming paradigms, and architectural platforms. United States.
Oliker, L., Li, X., Heber, G., and Biswas, R. Mon . "Parallel conjugate gradient: effects of ordering strategies, programming paradigms, and architectural platforms". United States. https://www.osti.gov/servlets/purl/775130.
@article{osti_775130,
title = {Parallel conjugate gradient: effects of ordering strategies, programming paradigms, and architectural platforms},
author = {Oliker, L. and Li, X. and Heber, G. and Biswas, R.},
abstractNote = {The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. A sparse matrix-vector multiply (SPMV) usually accounts for most of the floating-point operations with a CG iteration. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and SPMV using different programming and architectures. Results show that for this class of applications, ordering significantly improves overall performance, that cache reuse may be more important than reducing communication, and that it is possible to achieve message passing performance using shared memory constructs through careful data ordering and distribution. However, a multithreaded implementation of CG on the Tera MTA does not require special ordering or partitioning to obtain high efficiency and scalability.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2000},
month = {5}
}

Conference:
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