Multiscale collocation methods for ill-posed integral equations with a modified posteriori parameter selection (Q2411647)

The paper is concerned with multi-scale collocation schemes for ill-posed Fredholm integral equations which have applications in industrial and engineering. The idea presented is that collocation methods are attractive to engineers but that there is a bottleneck problem in choosing the regularisation parameters for solving ill-posed operator equations.. This paper proposes an a posteriori rule for choosing a regularisation parameter that ensures optimal convergence of the fast collocation methods described here. The paper concludes with numerical examples demonstrating the success of the approach.