On a quadratic eigenproblem occurring in regularized total least squares

In a recent paper Sima, Van Huffel and Golub [Regularized total least squares based on quadratic eigenvalue problem solvers. BIT Numerical Mathematics 44, 793 812 (2004)] suggested a computational approach for solving regularized total least squares problems via a sequence of quadratic eigenvalue problems. Taking advantage of a variational characterization of real eigenvalues of nonlinear eigenproblems we prove the existence of a right most eigenvalue. For large problems we improve the approach of Sima et al. considerably using thick and early updates in a nonlinear Arnoldi method.