Bound Constrained Regularization of Ill-Posed Problems

D. Dementiev and J. Nagy

We consider large scale ill-conditioned linear systems arising from discretization of ill-posed problems. Regularization is imposed through an (assumed known) upper bound constraint on the solution. An iterative scheme, requiring the computation of the smallest eigenvalue and corresponding eigenvector, is used to determine the proper level of regularization. In this paper we consider several computational issues involved in this approach, including the use of a Rayleigh quotient iteration for the eigenvalue/vector computation.