NEW PARTIALLY PROJECTIVE ALGORITHM FOR SPLIT FEASIBILITY PROBLEMS WITH APPLICATION TO BVP

Starting from the iterative process S-n, in this article we introduce a new three-step projective algorithm that aims to solve the split feasibility problem (SFP). To begin with, we give some aspects regarding the emergence of the SFP concept, as well as a detailed description of some preliminary theoretical tools. Then we move on to the main chapter of this paper which contains several results related to the convergence of the new procedure. Furthermore, we rephrase the finite difference method for a boundary value problem (BVP) connected to second order linear ODE as a split feasibility problem, under the assumption of controlled truncation errors. As an application of such an approach, we finally perform a numerical simulation on a particular BVP in order to emphasize the advantages of the newly introduced procedure over the classical CQ algorithm.