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This paper is interested at the Cauchy problem for Laplace's equation, which is to recover both Dirichlet and Neumann conditions on the inaccessible part of the boundary (inner part) of an annular domain from the over specified conditions on the accessible one (outer part). This work is an extension of the proposed algorithm for a unit circle  to annular domain, where, we describe an alternating formulation of the KMF algorithm proposed by Kozlov, Mazya and Fomin, and its relationship withdoi:10.4236/ajcm.2012.22012 fatcat:6rhoswak5zallnuuuaa4hv26dm