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The analysis for the total least squares problem with more than one solution. (English) Zbl 0758.65039
The paper generalizes the analysis of the solutions of the total least squares problem (TLS) \(AX\approx B\) to the case where the matrix \((A,B)\) may have multiple smallest singular values and to the rank-deficient case. Estimates for the difference between the LS and TLS solutions and perturbation bounds are given. Numerical experiments with an electromagnetic data processing problem show relative errors of about \(10^{-10}\) for the non-perturbed problem and of up to \(10^{-5}\) for a normally distributed perturbation with standard deviation \(10^{-10}\).

MSC:
65F20 Numerical solutions to overdetermined systems, pseudoinverses
65K05 Numerical mathematical programming methods
90C20 Quadratic programming
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