On a generalized matrix approximation problem in the spectral norm
Författare
Summary, in English
Abstract in Undetermined
In this paper theoretical results regarding a generalized minimum rank matrix approximation problem in the spectral norm are presented. An alternative solution expression for the generalized matrix approximation problem is obtained. This alternative expression provides a simple characterization of the achievableminimum rank, which is shown to be the same as the optimal objective value of the classical problem considered by Eckart–Young–Schmidt–Mirsky, as long as the generalized problem is feasible. In addition, this paper provides a result on a constrained version of the matrix approximation problem, establishing that the later problem is solvable via singular value decomposition.
In this paper theoretical results regarding a generalized minimum rank matrix approximation problem in the spectral norm are presented. An alternative solution expression for the generalized matrix approximation problem is obtained. This alternative expression provides a simple characterization of the achievableminimum rank, which is shown to be the same as the optimal objective value of the classical problem considered by Eckart–Young–Schmidt–Mirsky, as long as the generalized problem is feasible. In addition, this paper provides a result on a constrained version of the matrix approximation problem, establishing that the later problem is solvable via singular value decomposition.
Avdelning/ar
Publiceringsår
2012
Språk
Engelska
Sidor
2331-2341
Publikation/Tidskrift/Serie
Linear Algebra and Its Applications
Volym
436
Issue
7
Fulltext
- Available as PDF - 94 kB
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Dokumenttyp
Artikel i tidskrift
Förlag
Elsevier
Ämne
- Control Engineering
Nyckelord
- matrix approximation
- rank minimization
- singular value decomposition
Status
Published
Projekt
- LCCC
Forskningsgrupp
- LCCC
ISBN/ISSN/Övrigt
- ISSN: 1873-1856