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Parallelism in algebraic computation and parallel algorithms for symbolic linear systems

Authors:

Tateaki Sasaki,

Yasumasa KanadaAuthors Info & Claims

SYMSAC '81: Proceedings of the fourth ACM symposium on Symbolic and algebraic computation

Pages 160 - 167

https://doi.org/10.1145/800206.806388

Published: 05 August 1981 Publication History

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Abstract

Parallel execution of algebraic computation is discussed in the first half of this paper. It is argued that, although a high efficiency is obtained by parallel execution of divide-and-conquer algorithms, the ratio of the throughput to the number of processors is still small. Parallel processing will be most successful for the modular algorithms and many algorithms in linear algebra. In the second half of this paper, parallel algorithms for symbolic determinants and linear equations are proposed. The algorithms manifest a very high efficiency in a simple parallel processing scheme. These algorithms are well usable in also the serial processing scheme.

References

[1]

Enslow, P.H., "Multiprocessor organization - A Survey," Computing Surveys, Vol. 9, No. 1 (1977).

Digital Library

Google Scholar

[2]

Misunas, D.P., "Workshop on Data Flow Computer and Program Organization," Comp. Arch. News (ACM SIGARCH), Vol. 6, pp. 6-22 (1977).

Google Scholar

[3]

Backus, J., "Can Programming be Liberated from the von Neumann Style? A Functional Style and its Algebra of Programs," CACM, Vol. 21, pp. 613-641 (1978).

Digital Library

Google Scholar

[4]

Friedman, D.P. and Wise, D.S., "Aspects of Applicative Programming for Parallel Processing," IEEE Trans. Comp., Vol. c-27, pp. 289-296 (1978).

Digital Library

Google Scholar

[5]

Prini, G., "Explicit Parallelism in LISP-like Languages," Proc. LISP Conf., pp. 13-18 (1980).

Digital Library

Google Scholar

[6]

Marti, J.B., "Compilation Techniques for a Control-Flow Concurrent LISP System," Proc. LISP Conf., pp. 203-207 (1980).

Digital Library

Google Scholar

[7]

Yasui, H., Saito, T., Mitsuishi, A. and Miyazaki, Y., "Architecture of EVLIS Machine and Dynamic Measurements of Parallel Processing in LISP" (in Japanese), working paper of Kigoshori-Kenkyukai, IPS of Japan, (Dec. 1979); abstract in JIP. Vol. 2, p. 232 (1980).

Google Scholar

[8]

Yoshimura, S., Mizutani, H. and Shibayama, S., "A Parallel Processing Machine" (in Japanese), Collected Papers on Pattern Processing System -Natl. R & D Program, Agency of industrial Sci. and Tech. of Japan, pp. 211-222 (1980).

Google Scholar

[9]

Griss, M.L., "Efficient Expression Evaluation in Sparse Minor Expansion, Using Hashing and Deferred Evaluation," Proc. Hawaii Intl. Conf. on System Sciences, pp. 169-172 (1977).

Google Scholar

[10]

Wang, P.S., "On the Expansion of Symbolic Determinants," Proc. Hawaii Intl. Conf. on System Sciences, pp. 173-175 (1977).

Google Scholar

[11]

Tesler, L.G. and Enea, H.J., "A Language Design for Concurrent Processors," Proc. AFIPS Conf., pp. 291-293 (1968).

Google Scholar

[12]

Griss, M.L., "The Algebraic Solution of Sparse Linear Systems via Minor Expansion," ACM TOMS, Vol. 2, pp. 31-49 (1976).

Digital Library

Google Scholar

[13]

Sasaki, T., Kanada, Y. and Watanabe, S., "Calculation of Discriminants of High Degree Equations," Tokyo J. Math., (to appear).

Google Scholar

Cited By

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Duriqi BSnopçe HSalihu ALuma A(2024)An overview of parallel processing of rectangular determinant calculation2024 13th Mediterranean Conference on Embedded Computing (MECO)10.1109/MECO62516.2024.10577905(1-7)Online publication date: 11-Jun-2024
https://doi.org/10.1109/MECO62516.2024.10577905
Ponder C(1988)Parallelism and algorithms for algebraic manipulation: current workACM SIGSAM Bulletin10.1145/49456.4945722:3(7-14)Online publication date: 1-Jul-1988
https://dl.acm.org/doi/10.1145/49456.49457

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Parallelism in algebraic computation and parallel algorithms for symbolic linear systems

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Published In

SYMSAC '81: Proceedings of the fourth ACM symposium on Symbolic and algebraic computation

August 1981

248 pages

ISBN:0897910478

DOI:10.1145/800206

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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Association for Computing Machinery

New York, NY, United States

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Published: 05 August 1981

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Duriqi BSnopçe HSalihu ALuma A(2024)An overview of parallel processing of rectangular determinant calculation2024 13th Mediterranean Conference on Embedded Computing (MECO)10.1109/MECO62516.2024.10577905(1-7)Online publication date: 11-Jun-2024
https://doi.org/10.1109/MECO62516.2024.10577905
Ponder C(1988)Parallelism and algorithms for algebraic manipulation: current workACM SIGSAM Bulletin10.1145/49456.4945722:3(7-14)Online publication date: 1-Jul-1988
https://dl.acm.org/doi/10.1145/49456.49457

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