Blind Deconvolution: Errors, Errors Everywhere
Computing in Science and Engineering
Blind Deconvolution: A Matter of Norm
Computing in Science and Engineering
Overview of total least-squares methods
Signal Processing
Level choice in truncated total least squares
Computational Statistics & Data Analysis
IEEE Transactions on Knowledge and Data Engineering
Journal of Computational Physics
Supervised clustering via principal component analysis in a retrieval application
Proceedings of the Third International Workshop on Knowledge Discovery from Sensor Data
Computational Statistics & Data Analysis
Journal of Biomedical Imaging - Special issue on mathematical methods for images and surfaces
A weighted view on the partial least-squares algorithm
Automatica (Journal of IFAC)
Efficient determination of the hyperparameter in regularized total least squares problems
Applied Numerical Mathematics
Large-scale Tikhonov regularization of total least squares
Journal of Computational and Applied Mathematics
Regularized robust optimization: the optimal portfolio execution case
Computational Optimization and Applications
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The total least squares (TLS) method is a successful method for noise reduction in linear least squares problems in a number of applications. The TLS method is suited to problems in which both the coefficient matrix and the right-hand side are not precisely known. This paper focuses on the use of TLS for solving problems with very ill-conditioned coefficient matrices whose singular values decay gradually (so-called discrete ill-posed problems), where some regularization is necessary to stabilize the computed solution. We filter the solution by truncating the small singular values of the TLS matrix. We express our results in terms of the singular value decomposition (SVD) of the coefficient matrix rather than the augmented matrix. This leads to insight into the filtering properties of the truncated TLS method as compared to regularized least squares solutions. In addition, we propose and test an iterative algorithm based on Lanczos bidiagonalization for computing truncated TLS solutions.