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On a generalized matrix approximation problem in the spectral norm

Sou, Kin Cheong LU and Rantzer, Anders LU (2012) In Linear Algebra and Its Applications 436(7). p.2331-2341
Abstract (Swedish)
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.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
matrix approximation, rank minimization, singular value decomposition
in
Linear Algebra and Its Applications
volume
436
issue
7
pages
2331 - 2341
publisher
Elsevier
external identifiers
  • wos:000301083100036
  • scopus:84857121407
ISSN
1873-1856
DOI
10.1016/j.laa.2011.10.009
project
LCCC
language
English
LU publication?
yes
id
9ff37117-a72f-433b-a20f-131b5007472b (old id 2293514)
date added to LUP
2012-01-12 12:10:19
date last changed
2017-05-21 03:21:52
@article{9ff37117-a72f-433b-a20f-131b5007472b,
  abstract     = {<b>Abstract in Undetermined</b><br/><br>
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.},
  author       = {Sou, Kin Cheong and Rantzer, Anders},
  issn         = {1873-1856},
  keyword      = {matrix approximation,rank minimization,singular value decomposition},
  language     = {eng},
  number       = {7},
  pages        = {2331--2341},
  publisher    = {Elsevier},
  series       = {Linear Algebra and Its Applications},
  title        = {On a generalized matrix approximation problem in the spectral norm},
  url          = {http://dx.doi.org/10.1016/j.laa.2011.10.009},
  volume       = {436},
  year         = {2012},
}