A preconditioned Chebyshev iterative method for solving symmetric and unsymmetric linear systems

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 preconditioned form. 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.