Abstract:
A unified approach for regularized approximation methods for Fredholm integral equations of the first kind is presented.Convergence theorems are proved in both the Hilbert space setting and in the uniform norm; the rate is optimal in Hilbert space setting, and is the best known in uniform norm. The paper generalizes the well-known Ritz regularized methods and a recent paper of Groetsch (1990) so as to include the cases of norm approximation and the collectively compact approximation, and thus applicable to the so far unexplored regularized Nystrom methods.
