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Title: Parallel solution of sparse algebraic equations

Abstract

Two methods that have been studied in recent years for solving large, sparse sets of algebraic equations, the multiple factoring method and the W-matrix method, are shown to be two independent methods of explaining equivalent computational procedures. The forward and backward substitution part of these methods are investigated using parallel processing techniques on commercially available computers. The results are presented from testing the proposed methods on two local memory machines, the Intel iPSC/1 and iPSC/860 hypercubes, and a shared memory machine, the Sequent SymmetryS81. With the iPSC/1, which is characterized by its slow communication rate and high communication overhead for a short message, the best speedup obtained is less than 2.5, and that was with only 8 of the 16 available processors in use. The iPSC/860, a more advance model of the iPSC family, is even worse as far as these parallel methods are concerned. Much better results were obtained on the Sequent Symmetry where a speedup of 7.48 was obtained with 16 processors.

Authors:
 [1];  [2]
  1. Feng Chia Univ., Taichung (Taiwan, Province of China)
  2. Northwestern Univ., Evanston, IL (United States)
Publication Date:
OSTI Identifier:
7154349
Resource Type:
Journal Article
Journal Name:
IEEE Transactions on Power Systems (Institute of Electrical and Electronics Engineers); (United States)
Additional Journal Information:
Journal Volume: 9:2; Journal ID: ISSN 0885-8950
Country of Publication:
United States
Language:
English
Subject:
24 POWER TRANSMISSION AND DISTRIBUTION; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; EQUATIONS; NUMERICAL SOLUTION; HYPERCUBE COMPUTERS; PARALLEL PROCESSING; ALGEBRA; AUGMENTATION; MEMORY DEVICES; NUMERICAL ANALYSIS; TASK SCHEDULING; COMPUTERS; DATA PROCESSING; MATHEMATICS; PROCESSING; PROGRAMMING; 240100* - Power Systems- (1990-); 990200 - Mathematics & Computers

Citation Formats

Lin, S L, and Ness, J.E. Van. Parallel solution of sparse algebraic equations. United States: N. p., 1994. Web.
Lin, S L, & Ness, J.E. Van. Parallel solution of sparse algebraic equations. United States.
Lin, S L, and Ness, J.E. Van. 1994. "Parallel solution of sparse algebraic equations". United States.
@article{osti_7154349,
title = {Parallel solution of sparse algebraic equations},
author = {Lin, S L and Ness, J.E. Van},
abstractNote = {Two methods that have been studied in recent years for solving large, sparse sets of algebraic equations, the multiple factoring method and the W-matrix method, are shown to be two independent methods of explaining equivalent computational procedures. The forward and backward substitution part of these methods are investigated using parallel processing techniques on commercially available computers. The results are presented from testing the proposed methods on two local memory machines, the Intel iPSC/1 and iPSC/860 hypercubes, and a shared memory machine, the Sequent SymmetryS81. With the iPSC/1, which is characterized by its slow communication rate and high communication overhead for a short message, the best speedup obtained is less than 2.5, and that was with only 8 of the 16 available processors in use. The iPSC/860, a more advance model of the iPSC family, is even worse as far as these parallel methods are concerned. Much better results were obtained on the Sequent Symmetry where a speedup of 7.48 was obtained with 16 processors.},
doi = {},
url = {https://www.osti.gov/biblio/7154349}, journal = {IEEE Transactions on Power Systems (Institute of Electrical and Electronics Engineers); (United States)},
issn = {0885-8950},
number = ,
volume = 9:2,
place = {United States},
year = {Sun May 01 00:00:00 EDT 1994},
month = {Sun May 01 00:00:00 EDT 1994}
}