Convergence of an Alternating Method to Solve the Cauchy Problem for Poisson's Equation

This work concerns the development of iterative algorithms for the solution of the Cauchy problem for the Poisson equation. We accelerate the process proposed by Kozlov et al. V.A. Kozlov, V.G. Maz'ya and A.V. Fomin (1991). An iterative method for solving the Cauchy problem for elliptic equations. Comput. Maths. Phys. , 31 (1), 45-52.] by making use of a relaxation of the Dirichlet data. We provide theoretical justification of the convergence of the new algorithm, and present some results of numerical experiments with the method.