Regularized Total Least Squares Based on Quadratic Eigenvalue Problem Solvers

This paper presents a new computational approach for solving the Regularized Total Least Squares problem. The problem is formulated by adding a quadratic constraint to the Total Least Square minimization problem. Starting from the fact that a quadratically constrained Least Squares problem can be solved via a quadratic eigenvalue problem, an iterative procedure for solving the regularized Total Least Squares problem based on quadratic eigenvalue problems is presented. Discrete ill-posed problems are used as simulation examples in order to numerically validate the method.AMS subject classification (2000) 65F20, 65F30.Received March 2003. Revised November 2003. Accepted January 2004. Communicated by Per Christian Hansen.