Explain Sabine Van Huffel's work on total least squares.
Total least squares addresses situations where errors exist in all measured variables, not just the dependent ones as in ordinary least squares. My approach involves reformulating such problems as matrix problems, often solvable through singular value decomposition (SVD) or related matrix factorizations. The goal is to find a 'best fit' model by minimizing errors in both the data and the model parameters simultaneously, ensuring a more accurate representation when measurement inaccuracies are inherent.
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