On an algorithm for solving Fredholm integrals of the first kind

In this paper we use an iterative algorithm for solving Fredholm equations of the first kind. The basic algorithm and convergence properties are known under certain conditions, but we provide a simpler convergence proof without requiring the restrictive conditions that have previously been needed. Several examples of independent interest are given, including mixing density estimation and a first passage time density function involving Brownian motion. We also develop the basic algorithm to include functions which are not necessarily non-negative and, again, present illustrations.