On a generalized matrix approximation problem in the spectral norm
Author
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.
Department/s
Publishing year
2012
Language
English
Pages
2331-2341
Publication/Series
Linear Algebra and Its Applications
Volume
436
Issue
7
Full text
- Available as PDF - 94 kB
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Document type
Journal article
Publisher
Elsevier
Topic
- Control Engineering
Keywords
- matrix approximation
- rank minimization
- singular value decomposition
Status
Published
Project
- LCCC
Research group
- LCCC
ISBN/ISSN/Other
- ISSN: 1873-1856