A fast algorithm for the symmetric eigenvalue problem

J. J. Dongarra; D. C. Sorensen

doi:10.1109/ARITH.1985.6158944

A fast algorithm for the symmetric eigenvalue problem

J. J. Dongarra, D. C. Sorensen

Computer Science and Mathematics Div

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

3 Scopus citations

Abstract

The symmetric eigenvalue problem is one of the most fundamental problems of computational mathematics. It arises in many applications, and therefore represents an important area for algorithmic research. It is also one of the first eigenvalue problems for which reliable methods have been obtained. It would be surprising therefore, if a new method were to be found that would offer a significant improvement in execution time over the fundamental algorithms available in standard software packages such as EISPACK [7]. However, it is reasonable to expect that eigenvalue calculations might be accelerated through the use of parallel algorithms for parallel computers that are emerging. We shall present such an algorithm in this paper. The algorithm is able to exploit parallelism at all levels of the computation and is well suited to a variety of architectures. However, a pleasant bonus of this research is that the parallel algorithm, even when run in serial mode, is significantly faster than the best sequential algorithm on large problems, and is effective on moderate size (order ≥30) problems when run in serial mode.

Original language	English
Title of host publication	Proceedings - 7th Symposium on Computer Arithmetic, ARITH 1985
Editors	Kai Hwang
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	338-342
Number of pages	5
ISBN (Electronic)	0818606320
DOIs	https://doi.org/10.1109/ARITH.1985.6158944
State	Published - 1985
Event	7th IEEE Symposium on Computer Arithmetic, ARITH 1985 - Urbana, United States Duration: Jun 4 1985 → Jun 6 1985

Publication series

Name	Proceedings - Symposium on Computer Arithmetic

Conference

Conference	7th IEEE Symposium on Computer Arithmetic, ARITH 1985
Country/Territory	United States
City	Urbana
Period	06/4/85 → 06/6/85

Funding

Work supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research U.S. Department of Energy under Contracts W-S1-100-Eng-38 DE-AC05-840R21400 and DE-FG02-85ER 25001.

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10.1109/ARITH.1985.6158944

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title = "A fast algorithm for the symmetric eigenvalue problem",

abstract = "The symmetric eigenvalue problem is one of the most fundamental problems of computational mathematics. It arises in many applications, and therefore represents an important area for algorithmic research. It is also one of the first eigenvalue problems for which reliable methods have been obtained. It would be surprising therefore, if a new method were to be found that would offer a significant improvement in execution time over the fundamental algorithms available in standard software packages such as EISPACK [7]. However, it is reasonable to expect that eigenvalue calculations might be accelerated through the use of parallel algorithms for parallel computers that are emerging. We shall present such an algorithm in this paper. The algorithm is able to exploit parallelism at all levels of the computation and is well suited to a variety of architectures. However, a pleasant bonus of this research is that the parallel algorithm, even when run in serial mode, is significantly faster than the best sequential algorithm on large problems, and is effective on moderate size (order ≥30) problems when run in serial mode.",

author = "Dongarra, {J. J.} and Sorensen, {D. C.}",

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year = "1985",

doi = "10.1109/ARITH.1985.6158944",

language = "English",

series = "Proceedings - Symposium on Computer Arithmetic",

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}

Dongarra, JJ & Sorensen, DC 1985, A fast algorithm for the symmetric eigenvalue problem. in K Hwang (ed.), Proceedings - 7th Symposium on Computer Arithmetic, ARITH 1985., 6158944, Proceedings - Symposium on Computer Arithmetic, Institute of Electrical and Electronics Engineers Inc., pp. 338-342, 7th IEEE Symposium on Computer Arithmetic, ARITH 1985, Urbana, United States, 06/4/85. https://doi.org/10.1109/ARITH.1985.6158944

A fast algorithm for the symmetric eigenvalue problem. / Dongarra, J. J.; Sorensen, D. C.
Proceedings - 7th Symposium on Computer Arithmetic, ARITH 1985. ed. / Kai Hwang. Institute of Electrical and Electronics Engineers Inc., 1985. p. 338-342 6158944 (Proceedings - Symposium on Computer Arithmetic).

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

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AU - Sorensen, D. C.

PY - 1985

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N2 - The symmetric eigenvalue problem is one of the most fundamental problems of computational mathematics. It arises in many applications, and therefore represents an important area for algorithmic research. It is also one of the first eigenvalue problems for which reliable methods have been obtained. It would be surprising therefore, if a new method were to be found that would offer a significant improvement in execution time over the fundamental algorithms available in standard software packages such as EISPACK [7]. However, it is reasonable to expect that eigenvalue calculations might be accelerated through the use of parallel algorithms for parallel computers that are emerging. We shall present such an algorithm in this paper. The algorithm is able to exploit parallelism at all levels of the computation and is well suited to a variety of architectures. However, a pleasant bonus of this research is that the parallel algorithm, even when run in serial mode, is significantly faster than the best sequential algorithm on large problems, and is effective on moderate size (order ≥30) problems when run in serial mode.

AB - The symmetric eigenvalue problem is one of the most fundamental problems of computational mathematics. It arises in many applications, and therefore represents an important area for algorithmic research. It is also one of the first eigenvalue problems for which reliable methods have been obtained. It would be surprising therefore, if a new method were to be found that would offer a significant improvement in execution time over the fundamental algorithms available in standard software packages such as EISPACK [7]. However, it is reasonable to expect that eigenvalue calculations might be accelerated through the use of parallel algorithms for parallel computers that are emerging. We shall present such an algorithm in this paper. The algorithm is able to exploit parallelism at all levels of the computation and is well suited to a variety of architectures. However, a pleasant bonus of this research is that the parallel algorithm, even when run in serial mode, is significantly faster than the best sequential algorithm on large problems, and is effective on moderate size (order ≥30) problems when run in serial mode.

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A fast algorithm for the symmetric eigenvalue problem

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