Efficient determination of the hyperparameter in regularized total least squares problems

Abstract

The total least squares (TLS) method is a successful approach for linear problems if both the system matrix and the right-hand side are contaminated by some noise. For ill-posed TLS problems regularization is necessary to stabilize the computed solution. In this paper we suggest the use of the L-curve for the determination of the regularization parameter. The focus is on efficient implementation with particular emphasis on the reuse of information gained during the convergence history.