Finding eigenvalues and eigenvectors of unsymmetric matrices using a distributed-memory multiprocessor

G. A. Geist; G. J. Davis

doi:10.1016/0167-8191(90)90147-2

Finding eigenvalues and eigenvectors of unsymmetric matrices using a distributed-memory multiprocessor

G. A. Geist, G. J. Davis

National Center for Computational Scienc

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Distrubuted-memory parallel algorithms for finding the eigenvalues and eigenvectors of a dense unsymmetric matrix are given. While several parallel algorithms have been developed for symmetric matrices, 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 algoritm to compute the eigenvalues, and back transformations to compute the eigenvectors. Several modifications to our parallel QR algorithm, including ring communication, pipelining and delayed updating are discussed and compared. Results and timings are given.

Original language	English
Pages (from-to)	199-209
Number of pages	11
Journal	Parallel Computing
Volume	13
Issue number	2
DOIs	https://doi.org/10.1016/0167-8191(90)90147-2
State	Published - Feb 1990

Funding

* Research was supported by the Applied Mathematical Sciences Research Program of the Office of Energy Research, U.S. Department of Energy.

Keywords

INTEL iPSC/2
Linear algebra
hypercube multiprocessor
timing results
unsymmetric eigenvalue/eigenvector problem

Access to Document

10.1016/0167-8191(90)90147-2

Cite this

@article{40881bb2871140f6b43259e58c331e26,

title = "Finding eigenvalues and eigenvectors of unsymmetric matrices using a distributed-memory multiprocessor",

abstract = "Distrubuted-memory parallel algorithms for finding the eigenvalues and eigenvectors of a dense unsymmetric matrix are given. While several parallel algorithms have been developed for symmetric matrices, 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 algoritm to compute the eigenvalues, and back transformations to compute the eigenvectors. Several modifications to our parallel QR algorithm, including ring communication, pipelining and delayed updating are discussed and compared. Results and timings are given.",

keywords = "INTEL iPSC/2, Linear algebra, hypercube multiprocessor, timing results, unsymmetric eigenvalue/eigenvector problem",

author = "Geist, {G. A.} and Davis, {G. J.}",

year = "1990",

month = feb,

doi = "10.1016/0167-8191(90)90147-2",

language = "English",

volume = "13",

pages = "199--209",

journal = "Parallel Computing",

issn = "0167-8191",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - Finding eigenvalues and eigenvectors of unsymmetric matrices using a distributed-memory multiprocessor

AU - Geist, G. A.

AU - Davis, G. J.

PY - 1990/2

Y1 - 1990/2

N2 - Distrubuted-memory parallel algorithms for finding the eigenvalues and eigenvectors of a dense unsymmetric matrix are given. While several parallel algorithms have been developed for symmetric matrices, 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 algoritm to compute the eigenvalues, and back transformations to compute the eigenvectors. Several modifications to our parallel QR algorithm, including ring communication, pipelining and delayed updating are discussed and compared. Results and timings are given.

AB - Distrubuted-memory parallel algorithms for finding the eigenvalues and eigenvectors of a dense unsymmetric matrix are given. While several parallel algorithms have been developed for symmetric matrices, 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 algoritm to compute the eigenvalues, and back transformations to compute the eigenvectors. Several modifications to our parallel QR algorithm, including ring communication, pipelining and delayed updating are discussed and compared. Results and timings are given.

KW - INTEL iPSC/2

KW - Linear algebra

KW - hypercube multiprocessor

KW - timing results

KW - unsymmetric eigenvalue/eigenvector problem

UR - http://www.scopus.com/inward/record.url?scp=0025384076&partnerID=8YFLogxK

U2 - 10.1016/0167-8191(90)90147-2

DO - 10.1016/0167-8191(90)90147-2

M3 - Article

AN - SCOPUS:0025384076

SN - 0167-8191

VL - 13

SP - 199

EP - 209

JO - Parallel Computing

JF - Parallel Computing

IS - 2

ER -

Finding eigenvalues and eigenvectors of unsymmetric matrices using a distributed-memory multiprocessor

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this