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An Efficient Parallel Version of the Householder-QL Matrix Diagonalisation Algorithm

An Efficient Parallel Version of the Householder-QL Matrix Diagonalisation Algorithm
An Efficient Parallel Version of the Householder-QL Matrix Diagonalisation Algorithm
In this paper we report an effective parallelisation of the Householder routine for the reduction of a real symmetric matrix to tri-diagonal form and the QL algorithm for the diagonalisation of the resulting matrix. The Householder algorithm scales like $\alpha N^3/P+\beta N^2 \log_2(P)$ and the QL algorithm like $\gamma N^2 + \delta N^3/P$ as the number of processors $P$ is increased for fixed problem size. The constant parameters $\alpha$, $\beta$, $\gamma$ and $\delta$ are obtained empirically. When the eigenvalues only are required the Householder method scales as above while the QL algorithm remains sequential. The code is implemented in c in conjunction with the Message Passing Interface (MPI) libraries and verified on a sixteen node IBM SP2 and for real matrices that occur in the simulation of properties of crystaline materials
0167-8191
311-319
Reeve, JS
dd909010-7d44-44ea-83fe-a09e4d492618
Heath, M
aee4c988-75c5-4fdb-b21f-b571bb277384
Reeve, JS
dd909010-7d44-44ea-83fe-a09e4d492618
Heath, M
aee4c988-75c5-4fdb-b21f-b571bb277384

Reeve, JS and Heath, M (1999) An Efficient Parallel Version of the Householder-QL Matrix Diagonalisation Algorithm Parallel Computing, 25, (3), pp. 311-319.

Record type: Article

Abstract

In this paper we report an effective parallelisation of the Householder routine for the reduction of a real symmetric matrix to tri-diagonal form and the QL algorithm for the diagonalisation of the resulting matrix. The Householder algorithm scales like $\alpha N^3/P+\beta N^2 \log_2(P)$ and the QL algorithm like $\gamma N^2 + \delta N^3/P$ as the number of processors $P$ is increased for fixed problem size. The constant parameters $\alpha$, $\beta$, $\gamma$ and $\delta$ are obtained empirically. When the eigenvalues only are required the Householder method scales as above while the QL algorithm remains sequential. The code is implemented in c in conjunction with the Message Passing Interface (MPI) libraries and verified on a sixteen node IBM SP2 and for real matrices that occur in the simulation of properties of crystaline materials

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Published date: 1999
Organisations: EEE

Identifiers

Local EPrints ID: 251943
URI: http://eprints.soton.ac.uk/id/eprint/251943
ISSN: 0167-8191
PURE UUID: a3249294-1382-42d0-9686-ffc9a6ac3db7

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Date deposited: 14 Apr 2000
Last modified: 18 Jul 2017 10:07

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Author: JS Reeve
Author: M Heath

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