The total least squares (TLS) method is a successful approach for linear problems if both the matrix and the right hand side are contaminated by some noise. In a recent paper Sima, Van Huffel and Golub suggested an iterative method for solving regularized TLS problems, where in each iteration step a quadratic eigenproblem has to be solved. In this paper we prove its global convergence, and we present an efficient implementation using an iterative projection method with thick updates.
Lampe, J., & Voss, H. (2008). Global convergence of RTLSQEP: A solver of regularized total least squares problems via quadratic eigenproblems. Mathematical Modelling and Analysis, 13(1), 55-66. https://doi.org/10.3846/1392-6292.2008.13.55-66
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