Numerical tools for analysis and solution of Fredholm integral equations of the first kind

Abstract

The author surveys several numerical tools that can be used for the analysis and solution of systems of linear algebraic equations derived from Fredholm integral equations of the first kind. These tools are based on the singular value decomposition (SVD) and the generalized SVD, and they allow the user to study many details of the integral equation. The tools also aid the user in choosing a good regularization parameter that balances the influence of regularization and perturbation errors.