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

Summary. 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 with a finite dimensional approximation instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing compared with standard methods. Received September 16, 1998 / Revised version received August 4, 1999 / Published online August 2, 2000