The phenomenon of hysteresis is commonly encountered in the study of magnetic materials. The Preisach operator and its variants have been successfully used in the modeling of a physical system with hysteresis. In an application, one has to determine a density function for the Preisach operator using the input-output behavior of the system at hand. In this paper, we describe a method for numerically determining an approximation of the density function when there is not enough experimental data to uniquely solve for the density function. We also present numerical results where we estimate an approximate density function from data published in the literature for a magnetostrictive actuator and an electro-active polymer.