Thesis-1980-Demetriou.pdf (2.06 MB)

Generalized preconditioning strategies

Download (2.06 MB)
thesis
posted on 16.11.2017 by Ioannis C. Demetriou
Over the past decade Professor David J. Evans [1968] has suggested the use of ‘Preconditioning’ in iterative methods for solving large, sparse systems of linear equations, which arise from the finite difference approximations to the partial differential equations. Since then, certain aspects on preconditioning have appeared in the literature and a whole new theory constructed. The versatility of the preconditioning concept is shown by the stimulating exploration of new numerical algorithms and methods of their realization. The aim of this thesis is to emphasise in the theory we use and develop together with the practice we state. This study led to a new form of preconditioning, which has not yet appeared in the literature. Specifically, we consider the conditioning matrix factorized into two rectangular matrices, so as to develop a new preconditioned iterative method and its related properties as well. It requires the selection of two parameters to be applied, a preconditioning parameter at its optimal value and an acceleration parameter in such a fashion that a simultaneous displacement method is applicable. [Continues.]

History

School

  • Science

Department

  • Computer Science

Publisher

© Ioannis C. Demetriou

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 2.5 Generic (CC BY-NC-ND 2.5) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by-nc-nd/2.5/

Publication date

1980

Notes

A Master's Thesis. Submitted in partial fulfilment of the requirements for the award of Master of Philosophy at Loughborough University.

Language

en

Exports

Logo branding

Keyword(s)

Exports