On least squares solutions subject to a rank restriction

In this paper,we discuss rank-constrained least squares solutions to the matrix equation under the rank restriction in the Frobenius norm. We derive the rank range and expression of these least squares solutions by applying generalized inverses, singular value decomposition and the Eckart-Young-Mirs...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 63; no. 2; pp. 264 - 273
Main Author Wang, Hongxing
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.02.2015
Taylor & Francis Ltd
Subjects
Algebra
Constrictions
Decomposition
Economic models
least squares
Least squares method
Mathematical analysis
Norms
rank-constrained
singular value decomposition
Theorems
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Summary:In this paper,we discuss rank-constrained least squares solutions to the matrix equation under the rank restriction in the Frobenius norm. We derive the rank range and expression of these least squares solutions by applying generalized inverses, singular value decomposition and the Eckart-Young-Mirsky theorem.
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ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2013.860598