Alternating direction implicit preconditioning methods for self adjoint elliptic differential equations

AbstractIn this paper, the application of preconditioning to improve the convergence rates of iterative methods for solving large sparse linear systems of finite difference equations arising from the discretisation of elliptic partial differential equations of self adjoint form on a rectangular grid is extended to the alternating direction implicit (A. D. I) methods. Theoretical results are presented for the model problem