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Orthogonal least squares fitting with linear manifolds. (English) Zbl 0562.65008

The problem is considered of fitting a linear manifold of dimension s with \(1\leq s\leq n-1\) to a given set of points in \({\mathbb{R}}^ n\) such that the sum of orthogonal squared distances attains a minimum.

MSC:

65D10 Numerical smoothing, curve fitting
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References:

[1] Eckart, C., Young, G.: The Approximation of one Matrix by another of Lower Rank. Psychometrica1, 211-218 (1936) · JFM 62.1075.02 · doi:10.1007/BF02288367
[2] Golub. G.H., Loan, C.F. van: An Analysis of the Total Least Squares Problem. SIAM J. Numer. Anal.17, 883-893 (1980) · Zbl 0468.65011 · doi:10.1137/0717073
[3] Stewart, G.W.: A Generalization of the Eckart-Young Approximation Theorem. Report TR-1325, Department of Computer Science and Institute for Physical Science and Technology, The University of Maryland at College Park (1983)
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