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Extension of the total least square problem using general unitarily invariant norms. (English) Zbl 1112.65037
Using general unitarily invariant norms, the authors derive a formula that extends the total least squares problem. Their results cover the currently available results for the total least squares problem and the results given by K. B. Huang and S. J. Yan [Math. Numer. Sin. 19, 185–192 (1997; Zbl 0883.65033)]. They first outline some of the difficulties associated with the problem then state and prove several theorems to derive their results. They conclude the paper with a couple of interesting corollaries.

65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F35 Numerical computation of matrix norms, conditioning, scaling
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[1] DOI: 10.1137/0717073 · Zbl 0468.65011
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[3] Huang KB, Mathematica Numerica Sinica 19 pp 185– (1997)
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[9] DOI: 10.1093/qmath/11.1.50 · Zbl 0105.01101
[10] DOI: 10.1137/0613047 · Zbl 0758.65039
[11] DOI: 10.1007/BF01396223 · Zbl 0761.65030
[12] DOI: 10.1016/0024-3795(72)90013-4 · Zbl 0252.15009
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