On the existence of solutions to equality constrained least-squares problems in infinite-dimensional Hilbert spaces. (Q1855810)
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scientific article; zbMATH DE number 1861189
| Language | Label | Description | Also known as |
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| English | On the existence of solutions to equality constrained least-squares problems in infinite-dimensional Hilbert spaces. |
scientific article; zbMATH DE number 1861189 |
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On the existence of solutions to equality constrained least-squares problems in infinite-dimensional Hilbert spaces. (English)
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28 January 2003
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The least-squares problems with equality constraints \[ \min\| Tx-g\| , \text{ \;subject to }\| Sx-h\| =\min_{z\in X}\| Sz-h\| , \] for bounded linear operators with closed range in Hilbert spaces \(X, Y\) are considered. The author studies the problem of existence of solutions for all \(g, h \in Y\), based on results of \textit{R.~Bouldin} [Tôhoku Math. J., II. Ser. 25, 359-363 (1973; Zbl 0269.47002)]. Some necessary and sufficient conditions are given in terms of the angle between specified subspaces.
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least-squares problems
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equality constraints
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closed range
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existence of solutions
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angle between subspaces
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