Multilevel augmentation algorithms based on fast collocation methods for solving ill-posed integral equations

This paper continues the theme of the recent work Chen et al. (2008) [18], in which fast collocation methods are introduced for solving ill-posed Fredholm integral equations of the first kind. We develop in this paper multilevel augmentation algorithms, which lead to fast solutions of the discrete equations resulting from fast collocation methods. Regularization parameter choice strategies are given for proposed methods. The theoretical analysis and numerical experiments illustrate the accuracy and efficiency of the algorithm.