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

The aim of this paper is to describe an efficient adaptive strategy for discretizing ill-posed linear operator equations of the first kind: we consider Tikhonov-Phillips regularization x(alpha)(delta) = (A*A+alphaI)(-1) A*y(delta) with a finite 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.