Parallel computation of eigenvalues and eigenvectors using Occam and transputers
Parallel computation of eigenvalues and eigenvectors using Occam and transputers
The transputer is a fast microprocessor, unique in its linking ability to provide a framework for building general purpose parallel systems which rely on communication and are expandable to a very high degree. Occam, the transputer's official language, greatly simplifies the problem of programming large parallel systems by enabling each application to be expressed in terms of communicating sequential processes that can be mapped onto a single processor or alternatively onto many transputers. Matricial algorithms, which are the basis for many engineering and scientific computations, have in general a good degree of potential parallelism but they need to be adapted to this computational model based in communication rather than in a global memory system. In this thesis, algorithms for the computation of eigenvalues and eigenvectors of symmetric matrices are developed and tested in the supernode (a reconfigurable machine consisting of 17 T800 transputers). The opportunities for parallelism depend very much on the structure of the matrix (i.e, tridiagonal, banded, sparse, full) and on the solution required (only some or all eigenvalues, or also eigenvectors): the different parallel strategies that have been used reflect this diversity. The success of each parallel algorithm, expressed in terms of large speedups, depends on many processors being active, carrying out useful work, for most of the time (good load-balance) and on relatively small communication overheads. These goals have been achieved in the algorithms presented in this thesis: not only have good speedups been obtained in the practical tests with the supernode but also it has been shown by analysis that more processors can be efficiently used for matrices of larger sizes.
University of Southampton
1990
Ralha, Rui Manuel Silva
(1990)
Parallel computation of eigenvalues and eigenvectors using Occam and transputers.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
The transputer is a fast microprocessor, unique in its linking ability to provide a framework for building general purpose parallel systems which rely on communication and are expandable to a very high degree. Occam, the transputer's official language, greatly simplifies the problem of programming large parallel systems by enabling each application to be expressed in terms of communicating sequential processes that can be mapped onto a single processor or alternatively onto many transputers. Matricial algorithms, which are the basis for many engineering and scientific computations, have in general a good degree of potential parallelism but they need to be adapted to this computational model based in communication rather than in a global memory system. In this thesis, algorithms for the computation of eigenvalues and eigenvectors of symmetric matrices are developed and tested in the supernode (a reconfigurable machine consisting of 17 T800 transputers). The opportunities for parallelism depend very much on the structure of the matrix (i.e, tridiagonal, banded, sparse, full) and on the solution required (only some or all eigenvalues, or also eigenvectors): the different parallel strategies that have been used reflect this diversity. The success of each parallel algorithm, expressed in terms of large speedups, depends on many processors being active, carrying out useful work, for most of the time (good load-balance) and on relatively small communication overheads. These goals have been achieved in the algorithms presented in this thesis: not only have good speedups been obtained in the practical tests with the supernode but also it has been shown by analysis that more processors can be efficiently used for matrices of larger sizes.
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Published date: 1990
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Local EPrints ID: 461790
URI: http://eprints.soton.ac.uk/id/eprint/461790
PURE UUID: e2f33ef6-343c-4b65-9e74-b5c852659df3
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Date deposited: 04 Jul 2022 18:55
Last modified: 04 Jul 2022 18:55
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Author:
Rui Manuel Silva Ralha
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