In this thesis the application of preconditioning to the Chebyshev
iterative method is presented. Large, sparse, symmetric and unsymmetric
linear systems which are derived from the finite difference discretization
of second order (self-adjoint) partial differential equations over a
rectangular domain are obtained and solved by a second order iterative
method based on the scaled and translated Chebyshev polynomials in a
Further, using a formula previously given for the optimum preconditioning
parameter, an adaptive procedure is presented for deriving
this value efficiently for a variety of boundary value problems.
A numerical example is described and experimental results are
obtained which confirm the theory.
A Master's Thesis. Submitted in partial fulfilment of the requirements for the award of Master of Philosophy of Loughborough University.