On a quadratic eigenproblem occurring in regularized total least squares

Authors:
J. Lampe;H. Voss
Affiliations:
Institute of Numerical Simulation, Hamburg University of Technology, Schwarzenbergstrae 95, D-21071 Hamburg, Germany;Institute of Numerical Simulation, Hamburg University of Technology, Schwarzenbergstrae 95, D-21071 Hamburg, Germany
Venue:
Computational Statistics & Data Analysis
Year:
2007

Citing 7
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Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
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A Krylov Subspace Method for Quadratic Matrix Polynomials with Application to Constrained Least Squares Problems

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SOAR: A Second-order Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem

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On the Solution of the Tikhonov Regularization of the Total Least Squares Problem

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Finding a Global Optimal Solution for a Quadratically Constrained Fractional Quadratic Problem with Applications to the Regularized Total Least Squares

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Editorial: Total Least Squares and Errors-in-variables Modeling

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Accelerating the LSTRS Algorithm

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Efficient determination of the hyperparameter in regularized total least squares problems

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Large-scale Tikhonov regularization of total least squares

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Abstract

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.