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On a quadratic eigenproblem occurring in regularized total least squares. (English) Zbl 1393.15013
Summary: A computational approach for solving regularized total least squares problems via a sequence of quadratic eigenvalue problems has recently been proposed. Taking advantage of a variational characterization of real eigenvalues of nonlinear eigenproblems the existence of a real right-most eigenvalue for each quadratic eigenvalue problem in the sequence is proven. For large problems the approach is improved considerably utilizing information from the previous quadratic problems and early updates in a nonlinear Arnoldi method.

##### MSC:
 15A18 Eigenvalues, singular values, and eigenvectors 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 65F20 Numerical solutions to overdetermined systems, pseudoinverses 65F22 Ill-posedness and regularization problems in numerical linear algebra
##### Software:
VanHuffel; UTV; Regularization tools; ARPACK
Full Text:
##### References:
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