An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection

The aim of this paper is to describe an eecient adaptive strategy for discretizing ill-posed linear operator equations of the rst kind: we consider Tikhonov-Phillips regularization x = (A A + I) ?1 A y with a nite dimensional approximation A n instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing A n compared with standard methods.