research-article

A Highly Parallel Algorithm for Root Extraction

Authors:

L. H. JamiesonAuthors Info & Claims

IEEE Transactions on Computers, Volume 38, Issue 3

Pages 443 - 449

https://doi.org/10.1109/12.21130

Published: 01 March 1989 Publication History

Abstract

A parallel algorithm for extracting the roots of a polynomial is presented. The algorithm is based on Graeffe's method, which is rarely used in serial implementations, because it is slower than many common serial algorithms, but is particularly well suited to parallel implementation. Graeffe's method is an iterative technique, and parallelism is used to reduce the execution time per iteration. A high degree of parallelism is possible, and only simple interprocessor communication is required. For a degree-n polynomial executed on an (n+1)-processor SIMD machine, each iteration in the parallel algorithm has arithmetic complexity of approximately 2n and a communications overhead n. In general, arithmetic speedup is on the order of p/2 for a p-processor implementation.

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Cited By

Lucas KJana P(2010)Parallel algorithms for finding polynomial Roots on OTIS-torusThe Journal of Supercomputing10.1007/s11227-009-0312-754:2(139-153)Online publication date: 1-Nov-2010
https://dl.acm.org/doi/10.1007/s11227-009-0312-7
Petković MIlić SPetković I(2007)A posteriori error bound methods for the inclusion of polynomial zerosJournal of Computational and Applied Mathematics10.1016/j.cam.2006.09.014208:2(316-330)Online publication date: 20-Nov-2007
https://dl.acm.org/doi/10.1016/j.cam.2006.09.014
Jana P(2006)Polynomial interpolation and polynomial root finding on OTIS-meshParallel Computing10.1016/j.parco.2006.01.00132:4(301-312)Online publication date: 1-Apr-2006
https://dl.acm.org/doi/10.1016/j.parco.2006.01.001

Index Terms

A Highly Parallel Algorithm for Root Extraction
1. Computing methodologies
  1. Parallel computing methodologies
    1. Parallel algorithms
2. Theory of computation
  1. Design and analysis of algorithms
    1. Parallel algorithms

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Published In

cover image IEEE Transactions on Computers

IEEE Transactions on Computers Volume 38, Issue 3

March 1989

166 pages

ISSN:0018-9340

Editor:
M. T. Liu
Ohio State Univ., Columbus

Issue’s Table of Contents

Copyright © Copyright © 1989 IEEE. All Rights Reserved.

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IEEE Computer Society

United States

Publication History

Published: 01 March 1989

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Cited By

Lucas KJana P(2010)Parallel algorithms for finding polynomial Roots on OTIS-torusThe Journal of Supercomputing10.1007/s11227-009-0312-754:2(139-153)Online publication date: 1-Nov-2010
https://dl.acm.org/doi/10.1007/s11227-009-0312-7
Petković MIlić SPetković I(2007)A posteriori error bound methods for the inclusion of polynomial zerosJournal of Computational and Applied Mathematics10.1016/j.cam.2006.09.014208:2(316-330)Online publication date: 20-Nov-2007
https://dl.acm.org/doi/10.1016/j.cam.2006.09.014
Jana P(2006)Polynomial interpolation and polynomial root finding on OTIS-meshParallel Computing10.1016/j.parco.2006.01.00132:4(301-312)Online publication date: 1-Apr-2006
https://dl.acm.org/doi/10.1016/j.parco.2006.01.001

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