A comparison of rates of convergence for the Modified Alternating Direction Preconditioning (MADP) method

This paper considers the numerical solution of the elliptic self-adjoint second order and the biharmonic equations using a variety of accelerated versions of the Modified Alternating Direction Preconditioning (MADP) method developed in [4]. The resulting iterative schemes possess rates of convergence which are improved by an order of magnitude as compared with the well known ADI methods. Finally, a survey of numerical experiments and comparisons with existing results, concerned with the solution of Laplace and biharmonic equations in the unit square, are also reported.