Solving Fredholm Integral Equations of the Second Kind via Wasserstein Gradient Flows
<|reference_start|>Solving Fredholm Integral Equations of the Second Kind via Wasserstein Gradient Flows: 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.<|reference_end|>
@article{crucinio2024solving,
    title={Solving Fredholm Integral Equations of the Second Kind via Wasserstein
  Gradient Flows},
    author={Francesca R. Crucinio, Adam M. Johansen},
    journal={arXiv preprint arXiv:2409.19642},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.19642},
    primaryClass={stat.CO cs.NA math.NA math.OC stat.ME}
}