An algorithm for determining a rational function that approximates a holomorphic function on a domain of the complex plane is described. One application the authors have in mind is the construction of a concise description of a discrete time system. Several theorems are given on the existence and uniqueness of solutions to the problem posed. A fairly detailed conceptual algorithm is presented, but no numerical examples are reported. The style of this research paper is fairly technical, and the reader is supposed to master both the theory of analytic functions and some functional analysis. The list of references is adequate.