The algebraic eigenvalue problem occurring in a variety of problems
in the Natural, Engineering and Social Sciences areas can with some
advantage be solved by matrix methods. However, these problems become more
difficult to handle when the matrices involved are large and sparse because
the storage and manipulations of these types of matrices have to be achieved
in such ways that firstly, no storage is wasted by retaining the zero
elements of the matrix and secondly, saving valuable computer time by not
operating on the zero elements when unnecessary. For this purpose, we have
previously developed a software package on the storage and manipulation of
sparse matrices, which consists of basic matrix operations
(i.e. addition, multiplication, etc.) and the solution of linear systems
by iterative methods. However, in that work we encountered a great deal of
difficulty in handling the operations which generate non-zero elements
during processes such as the Gaussian elimination process. [Continues.]
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.
Loughborough University of Technology, Department of Computer Studies.