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

311-319

Reeve, JS

dd909010-7d44-44ea-83fe-a09e4d492618

Heath, M

aee4c988-75c5-4fdb-b21f-b571bb277384

1999

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), .

## 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

**Postscript paper.ps
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## More information

Published date: 1999

Organisations:
EEE

## Identifiers

Local EPrints ID: 251943

URI: https://eprints.soton.ac.uk/id/eprint/251943

ISSN: 0167-8191

PURE UUID: a3249294-1382-42d0-9686-ffc9a6ac3db7

## Catalogue record

Date deposited: 14 Apr 2000

Last modified: 18 Jul 2017 10:07

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## Contributors

Author:
JS Reeve

Author:
M Heath

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