Iterative methods are considered for the numerical solution of large, sparse, nonsingular, and nonsymmetric systems of linear equations Ax=b, where it is also required that A is p-cyclic (p≥2). Firstly, it is shown that the SOR method applied to the system with A as p-cyclic, if p>2, has a slower rate of convergence than the SOR method applied to the same system with A considered as 2-cyclic under some conditions. Therefore, the p-cyclic matrix A should be partitioned into 2-cyclic form when the SOR method is applied. [Continues.]
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.