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Prefix algorithms for tridiagonal systems on hypercube multiprocessors

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A. J. LaubAuthors Info & Claims

C³P: Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2

Pages 1539 - 1545

https://doi.org/10.1145/63047.63112

Published: 03 January 1989 Publication History

Abstract

The recursive doubling algorithm as developed by Stone can be used to solve a tridiagonal linear system of size n on a parallel computer with n processors using Ο ( log n ) parallel arithmetic steps. Here we describe a limited processor version of the recursive doubling algorithm for the solution of tridiagonal linear systems using Ο ( n / p + log p ) parallel arithmetic steps on a parallel computer with p < n processors. The main technique relies on fast parallel prefix algorithms, which can be efficiently mapped on the hypercube architecture using the binary-reflected Gray code. For pn this algorithm achieves linear speed-up and constant efficiency over its sequential implementation as well as over the sequential LU decomposition algorithm. These results are confirmed by numerical experiments obtained on an Intel iPSC/d5 hypercube multiprocessor.

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Cited By

Fox G(1989)What have we learnt from using real parallel machines to solve real problems?Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 210.1145/63047.63048(897-955)Online publication date: 3-Jan-1989
https://dl.acm.org/doi/10.1145/63047.63048

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Prefix algorithms for tridiagonal systems on hypercube multiprocessors

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cover image ACM Conferences

C³P: Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2

January 1989

1787 pages

ISBN:0897912780

DOI:10.1145/63047

Editor:
Geoffrey Fox
California Institute of Technology, Pasadena, CA

Copyright © 1989 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 03 January 1989

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Fox G(1989)What have we learnt from using real parallel machines to solve real problems?Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 210.1145/63047.63048(897-955)Online publication date: 3-Jan-1989
https://dl.acm.org/doi/10.1145/63047.63048

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