On an algorithm for solving Fredholm integrals of the first kind

Minwoo Chae, Ryan Martin, Stephen G. Walker

Abstract: 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.