Three-Point boundary value problems associated with first order matrix difference system-existence and uniqueness via shortest and closest Lattice vector methods

In this paper, we shall be concerned with the existence and uniqueness of solution to three- point boundary value problems associated with a system of first order matrix difference system. Shortest and Closest Lattice vector methods are used as a tool to obtain the best least square solution of the three-point boundary value problem when the characteristic matrix D is rectangular. An efficient decode algorithm is presented to find the shortest and closest vector and prove that this vector is the best least square solution of the three-point boundary value problem.