On Low Rank Approximation of Linear Operators in p-Norms and Some Algorithms

Yang Liu ()
Additional contact information
Yang Liu: Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

Asia-Pacific Journal of Operational Research (APJOR), 2016, vol. 33, issue 04, 1-12

Abstract: In this paper, we study the optimal or best approximation of any linear operator by low rank linear operators, especially, any linear operator on the ℓp-space, p ∈ [1,∞), under ℓp norm, or in Minkowski distance. Considering generalized singular values and using techniques from differential geometry, we extend the classical Schmidt–Mirsky theorem in the direction of the ℓp-norm of linear operators for some p values. Also, we develop and provide algorithms for finding the solution to the low rank approximation problems in some nontrivial scenarios. The results can be applied to, in particular, matrix completion and sparse matrix recovery.

Keywords: Matrices; normed spaces; singular values; operator theory (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0217595916500238
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:apjorx:v:33:y:2016:i:04:n:s0217595916500238

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0217595916500238

Access Statistics for this article

Asia-Pacific Journal of Operational Research (APJOR) is currently edited by Gongyun Zhao

More articles in Asia-Pacific Journal of Operational Research (APJOR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().