On a quadratic eigenproblem occurring in regularized total least squares
Computational Statistics & Data Analysis
A generalized global Arnoldi method for ill-posed matrix equations
Journal of Computational and Applied Mathematics
Efficient determination of the hyperparameter in regularized total least squares problems
Applied Numerical Mathematics
Tikhonov regularization based on generalized Krylov subspace methods
Applied Numerical Mathematics
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We present a Krylov subspace--type projection method for a quadratic matrix polynomial $\lambda^2 I -\lambda A - B$ that works directly with A and B without going through any linearization. We discuss a special case when one matrix is a low rank perturbation of the other matrix. We also apply the method to solve quadratically constrained linear least squares problem through a reformulation of Gander, Golub, and von Matt as a quadratic eigenvalue problem, and we demonstrate the effectiveness of this approach. Numerical examples are given to illustrate the efficiency of the algorithms.