Thesis-1990-Levin.pdf (3.13 MB)
Parallel algorithms for SIMD and MIMD computers
thesis
posted on 2018-05-15, 08:36 authored by Matthew D. LevinThe thesis is concerned with the inversion of matrices and the solution of linear systems
and eigensystems in a parallel environment.
Following an introductory chapter of concepts and definitions in the field of linear
algebra, a general survey of parallel machines and algorithms is presented in Chapters 2
and 3, including a detailed description of the Distributed Array Processor (DAP) and the
Neptune multiprocessing system.
In Chapter 4, a new technique, the double-bordering algorithm, for the solution of
linear systems is derived, and its application to the parallel solution of difference systems
described. A modified form of the method for the inversion of matrices is derived,
implemented on the Neptune multiprocessing system, and its performance compared with
that of the Gauss-Jordan and (single) bordering algorithms. The results of the
implementation of several other parallel algorithms are also presented.
Chapter 5 deals with the class of matrices known as Toeplitz matrices, which arise in
the field of signal processing. Trench's algorithm for the inversion of such matrices is
implemented on the Neptune multiprocessing system, and, for the solution of banded
symmetric Toeplitz systems, the relative efficiencies of three sequential strategies are
compared: Levinson's algorithm, the double-bordering algorithm, and a method based on a
novel factorisation scheme.
Chapter 6 is concerned with the implementation of various iterative methods on the
DAP. The solution of several difference systems by the Jacobi, Gauss-Seidel and
successive over-relaxation (SOR) algorithms is compared with their solution by a variation
(c. 1943) of the algorithms proposed by Hotelling, in which matrix-vector products are
replaced by successive matrix squarings. The technique is also applied to the power
method for the solution of the eigenvalue problem.
The thesis concludes with a summary and recommendations for future work.
Funding
Science and Engineering Research Council.
History
School
- Science
Department
- Computer Science
Publisher
© M.D. LevinPublisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
1990Notes
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.Language
- en