Large-scale Tikhonov regularization of total least squares

Abstract

The total least squares (TLS) method is a successful approach for linear problems when not only the right-hand side but the system matrix is also contaminated by some noise. For ill-posed TLS problems regularization is necessary to stabilize the computed solution. In this paper we present a new approach for computing an approximate solution of the Tikhonov-regularized large-scale total least-squares problem. An iterative method is proposed which solves a convergent sequence of projected linear systems and thereby builds up a highly suitable search space. The focus is on efficient implementation with particular emphasis on the reuse of information.