Solving Fredholm Integral Equations of the Second Kind via Wasserstein Gradient Flows
Computation
2026-02-19 v3 Numerical Analysis
Numerical Analysis
Optimization and Control
Methodology
Abstract
Motivated by a recent method for approximate solution of Fredholm equations of the first kind, we develop a corresponding method for a class of Fredholm equations of the \emph{second kind}. In particular, we consider the class of equations for which the solution is a probability measure. The approach centres around specifying a functional whose gradient flow admits a minimizer corresponding to a regularized version of the solution of the underlying equation and using a mean-field particle system to approximately simulate that flow. Theoretical support for the method is presented, along with some illustrative numerical results.
Keywords
Cite
@article{arxiv.2409.19642,
title = {Solving Fredholm Integral Equations of the Second Kind via Wasserstein Gradient Flows},
author = {Francesca R. Crucinio and Adam M. Johansen},
journal= {arXiv preprint arXiv:2409.19642},
year = {2026}
}