Overview of total least-squares methods
Signal Processing
Level choice in truncated total least squares
Computational Statistics & Data Analysis
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For any linear system $A x \approx b$ we define a set of core problems and show that the orthogonal upper bidiagonalization of $[b, A]$ gives such a core problem. In particular we show that these core problems have desirable properties such as minimal dimensions. When a total least squares problem is solved by first finding a core problem, we show the resulting theory is consistent with earlier generalizations, but much simpler and clearer. The approach is important for other related solutions and leads, for example, to an elegant solution to the data least squares problem. The ideas could be useful for solving ill-posed problems.