On a generalized matrix approximation problem in the spectral norm
(2012) In Linear Algebra and Its Applications 436(7). p.2331-2341- Abstract
- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2293514
- author
- Sou, Kin Cheong LU and Rantzer, Anders LU
- organization
- publishing date
- 2012
- 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
- additional info
- key=sou_ran2011LAA month=November
- id
- 9ff37117-a72f-433b-a20f-131b5007472b (old id 2293514)
- date added to LUP
- 2016-04-01 10:56:51
- date last changed
- 2024-02-05 17:16:12
@article{9ff37117-a72f-433b-a20f-131b5007472b, abstract = {{Abstract in Undetermined<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}}, keywords = {{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 = {{https://lup.lub.lu.se/search/files/2260898/2293516.pdf}}, doi = {{10.1016/j.laa.2011.10.009}}, volume = {{436}}, year = {{2012}}, }