The impact of parallel architectures on the solution of eigenvalue problems

Ilse C.F. Ipsen; Youcef Saad

doi:10.1016/S0304-0208(08)72638-0

The impact of parallel architectures on the solution of eigenvalue problems

Ilse C.F. Ipsen
, Youcef Saad

Computer Science and Engineering

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

2 Scopus citations

Abstract

This paper presents a short survey of recent work on parallel implementations of Numerical Linear Algebra algorithms with emphasis on those relating to the solution of the symmetric eigenvalue problem on loosely coupled multiprocessor architectures. The vital operations in the formulation of most eigenvalue algorithms are matrix vector multiplication, matrix transposition, and linear system solution. Their implementations on several representative multiprocessor systems will be described, as well as parallel implementations of the following classes of eigenvalue methods : QR, bisection, divide-and-conquer, and Lanczos algorithm.

Original language	English (US)
Pages (from-to)	37-49
Number of pages	13
Journal	North-Holland Mathematics Studies
Volume	127
Issue number	C
DOIs	https://doi.org/10.1016/S0304-0208(08)72638-0
State	Published - Jan 1986

Bibliographical note

Funding Information:
The work presented in this paper was supported by the Office of Naval Research under contracts N000014-82-K-0184 and N00014-85-K-0461.

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10.1016/S0304-0208(08)72638-0

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abstract = "This paper presents a short survey of recent work on parallel implementations of Numerical Linear Algebra algorithms with emphasis on those relating to the solution of the symmetric eigenvalue problem on loosely coupled multiprocessor architectures. The vital operations in the formulation of most eigenvalue algorithms are matrix vector multiplication, matrix transposition, and linear system solution. Their implementations on several representative multiprocessor systems will be described, as well as parallel implementations of the following classes of eigenvalue methods : QR, bisection, divide-and-conquer, and Lanczos algorithm.",

author = "Ipsen, \{Ilse C.F.\} and Youcef Saad",

note = "Funding Information: The work presented in this paper was supported by the Office of Naval Research under contracts N000014-82-K-0184 and N00014-85-K-0461.",

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AU - Ipsen, Ilse C.F.

AU - Saad, Youcef

N1 - Funding Information: The work presented in this paper was supported by the Office of Naval Research under contracts N000014-82-K-0184 and N00014-85-K-0461.

PY - 1986/1

Y1 - 1986/1

N2 - This paper presents a short survey of recent work on parallel implementations of Numerical Linear Algebra algorithms with emphasis on those relating to the solution of the symmetric eigenvalue problem on loosely coupled multiprocessor architectures. The vital operations in the formulation of most eigenvalue algorithms are matrix vector multiplication, matrix transposition, and linear system solution. Their implementations on several representative multiprocessor systems will be described, as well as parallel implementations of the following classes of eigenvalue methods : QR, bisection, divide-and-conquer, and Lanczos algorithm.

AB - This paper presents a short survey of recent work on parallel implementations of Numerical Linear Algebra algorithms with emphasis on those relating to the solution of the symmetric eigenvalue problem on loosely coupled multiprocessor architectures. The vital operations in the formulation of most eigenvalue algorithms are matrix vector multiplication, matrix transposition, and linear system solution. Their implementations on several representative multiprocessor systems will be described, as well as parallel implementations of the following classes of eigenvalue methods : QR, bisection, divide-and-conquer, and Lanczos algorithm.

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UR - https://www.scopus.com/pages/publications/77956905127#tab=citedBy

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JO - North-Holland Mathematics Studies

JF - North-Holland Mathematics Studies

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ER -

The impact of parallel architectures on the solution of eigenvalue problems

Abstract

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