Browse by author
Lookup NU author(s): Professor Chris Phillips
We are concerned here with the solution of the system of linear equations Ax = b, (1) with A an n x n matrix and x and b conforming n-vectors. Of particular interest is the situation in which n is large (of the order of 1000's) and A is sparse; linear systems with such properties arise from, for example, 'the discretisation' of elliptic partial differential equations using finite difference or finite element techniques. (see [1] for a review of numerical methods for partial differential equations on vector and parallel computers and a discussion of application areas.) It is theoretically possible to solve systems of this form using direct methods based on elimination techniques (see [2] for a parallel implementation in the case that A is symmetric and positive definite and [3] for a more general discussion) but this approach can be very expensive both in terms of storage requirements and computation. This is a direct consequence of the fill-in that may occur. An alternative, and frequently used, approach which avoids these drawbacks is based on the use of iteration, leading to a family of (Krylov subspace) methods which cover the various particular forms that A may take.
Author(s): Cook R, Phillips C
Publication type: Report
Publication status: Published
Series Title: Department of Computing Science Technical Report Series
Year: 1994
Pages: 10
Print publication date: 01/03/1994
Source Publication Date: March 1994
Report Number: 473
Institution: Department of Computing Science, University of Newcastle upon Tyne
Place Published: Newcastle upon Tyne
URL: http://www.cs.ncl.ac.uk/publications/trs/papers/473.pdf
