Finding eigenvalues and eigenvectors of unsymmetric matrices using a hypercube multiprocessor

G. A. Geist; R. C. Ward; G. J. Davis; R. E. Funderlic

doi:10.1145/63047.63118

Finding eigenvalues and eigenvectors of unsymmetric matrices using a hypercube multiprocessor

G. A. Geist, R. C. Ward, G. J. Davis, R. E. Funderlic

National Center for Computational Scienc

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

11 Scopus citations

Abstract

Distributed-memory algorithms for finding the eigenvalues and eigenvectors of a dense unsymmetric matrix are given. While several parallel algorithms have been developed for symmetric systems, little work has been done on the unsymmetric case. Our parallel implementation proceeds in three major steps: reduction of the original matrix to Hessenberg form, application of the implicit double-shift QR algorithm to compute the eigenvalues, and back transformations to compute the eigenvectors. Several modifications to our parallel QR algorithm, including ring communication and pipelining, are discussed and compared. Results and timings are given.

Original language	English
Title of host publication	Proceedings of the 3rd Conference on Hypercube Concurrent Computers and Applications, C3P 1988
Editors	Geoffrey Fox
Publisher	Association for Computing Machinery, Inc
Pages	1577-1582
Number of pages	6
ISBN (Electronic)	0897912780, 9780897912785
DOIs	https://doi.org/10.1145/63047.63118
State	Published - Jan 3 1989
Event	3rd Conference on Hypercube Concurrent Computers and Applications, C3P 1988 - Pasadena, United States Duration: Jan 19 1988 → Jan 20 1988

Publication series

Name	Proceedings of the 3rd Conference on Hypercube Concurrent Computers and Applications: Architecture, Software, Computer Systems, and General Issues, C3P 1988
Volume	2

Conference

Conference	3rd Conference on Hypercube Concurrent Computers and Applications, C3P 1988
Country/Territory	United States
City	Pasadena
Period	01/19/88 → 01/20/88

Funding

*This research was supported by the Applied Mathematical Sciences Research Program, Office of Energy Research, U.S. Department of Energy under contract DE-AC05-840R21400 with Martin Marietta Energy Systems Inc.

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10.1145/63047.63118

Cite this

Geist, G. A., Ward, R. C., Davis, G. J., & Funderlic, R. E. (1989). Finding eigenvalues and eigenvectors of unsymmetric matrices using a hypercube multiprocessor. In G. Fox (Ed.), Proceedings of the 3rd Conference on Hypercube Concurrent Computers and Applications, C3P 1988 (pp. 1577-1582). (Proceedings of the 3rd Conference on Hypercube Concurrent Computers and Applications: Architecture, Software, Computer Systems, and General Issues, C3P 1988; Vol. 2). Association for Computing Machinery, Inc. https://doi.org/10.1145/63047.63118

Geist, G. A. ; Ward, R. C. ; Davis, G. J. et al. / Finding eigenvalues and eigenvectors of unsymmetric matrices using a hypercube multiprocessor. Proceedings of the 3rd Conference on Hypercube Concurrent Computers and Applications, C3P 1988. editor / Geoffrey Fox. Association for Computing Machinery, Inc, 1989. pp. 1577-1582 (Proceedings of the 3rd Conference on Hypercube Concurrent Computers and Applications: Architecture, Software, Computer Systems, and General Issues, C3P 1988).

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abstract = "Distributed-memory algorithms for finding the eigenvalues and eigenvectors of a dense unsymmetric matrix are given. While several parallel algorithms have been developed for symmetric systems, little work has been done on the unsymmetric case. Our parallel implementation proceeds in three major steps: reduction of the original matrix to Hessenberg form, application of the implicit double-shift QR algorithm to compute the eigenvalues, and back transformations to compute the eigenvectors. Several modifications to our parallel QR algorithm, including ring communication and pipelining, are discussed and compared. Results and timings are given.",

author = "Geist, {G. A.} and Ward, {R. C.} and Davis, {G. J.} and Funderlic, {R. E.}",

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Geist, GA, Ward, RC, Davis, GJ & Funderlic, RE 1989, Finding eigenvalues and eigenvectors of unsymmetric matrices using a hypercube multiprocessor. in G Fox (ed.), Proceedings of the 3rd Conference on Hypercube Concurrent Computers and Applications, C3P 1988. Proceedings of the 3rd Conference on Hypercube Concurrent Computers and Applications: Architecture, Software, Computer Systems, and General Issues, C3P 1988, vol. 2, Association for Computing Machinery, Inc, pp. 1577-1582, 3rd Conference on Hypercube Concurrent Computers and Applications, C3P 1988, Pasadena, United States, 01/19/88. https://doi.org/10.1145/63047.63118

Finding eigenvalues and eigenvectors of unsymmetric matrices using a hypercube multiprocessor. / Geist, G. A.; Ward, R. C.; Davis, G. J. et al.
Proceedings of the 3rd Conference on Hypercube Concurrent Computers and Applications, C3P 1988. ed. / Geoffrey Fox. Association for Computing Machinery, Inc, 1989. p. 1577-1582 (Proceedings of the 3rd Conference on Hypercube Concurrent Computers and Applications: Architecture, Software, Computer Systems, and General Issues, C3P 1988; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - Distributed-memory algorithms for finding the eigenvalues and eigenvectors of a dense unsymmetric matrix are given. While several parallel algorithms have been developed for symmetric systems, little work has been done on the unsymmetric case. Our parallel implementation proceeds in three major steps: reduction of the original matrix to Hessenberg form, application of the implicit double-shift QR algorithm to compute the eigenvalues, and back transformations to compute the eigenvectors. Several modifications to our parallel QR algorithm, including ring communication and pipelining, are discussed and compared. Results and timings are given.

AB - Distributed-memory algorithms for finding the eigenvalues and eigenvectors of a dense unsymmetric matrix are given. While several parallel algorithms have been developed for symmetric systems, little work has been done on the unsymmetric case. Our parallel implementation proceeds in three major steps: reduction of the original matrix to Hessenberg form, application of the implicit double-shift QR algorithm to compute the eigenvalues, and back transformations to compute the eigenvectors. Several modifications to our parallel QR algorithm, including ring communication and pipelining, are discussed and compared. Results and timings are given.

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Geist GA, Ward RC, Davis GJ, Funderlic RE. Finding eigenvalues and eigenvectors of unsymmetric matrices using a hypercube multiprocessor. In Fox G, editor, Proceedings of the 3rd Conference on Hypercube Concurrent Computers and Applications, C3P 1988. Association for Computing Machinery, Inc. 1989. p. 1577-1582. (Proceedings of the 3rd Conference on Hypercube Concurrent Computers and Applications: Architecture, Software, Computer Systems, and General Issues, C3P 1988). doi: 10.1145/63047.63118

Finding eigenvalues and eigenvectors of unsymmetric matrices using a hypercube multiprocessor

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