Two projection methods for Regularized Total Least Squares approximation

Regularized Total Least Squares is a useful approach for solving ill-posed overdetermined systems of equations when both the model matrix and the observed data are contaminated by noise. A Newton-based Regularized Total Least Squares method was proposed by Lee et al. (2013) [16], but may not be efficient for large scale problems. Here we consider two projection-based algorithms applied to this method for the solution of the large scale problem. The first fixes the underlying subspace dimension, while the second expands the subspace dynamically during the iterations by employing a generalized Krylov subspace expansion. Experimental results demonstrate that the two projection-based algorithms can be successfully applied for the solution of the large scale Regularized Total Least Squares problems.