Two simple proofs for analyticity of the central path in linear programming

Several papers have appeared recently establishing the analyticity of the central path at the boundary point for both linear programming (LP) and linear complementarity problems (LCP). While the proofs for LP are long, proceeding from limiting properties of the corresponding derivatives, the proofs for LCP are very simple, consisting of an application of the implicit function theorem to a certain system of equations. Inspired by the approach for LCP, this paper gives two simple ways of proving the analyticity of the central path for LP. One follows the idea for LCP, the other is based on a proper partition of the system defining the central path.