The Sparsity of Underdetermined Linear System via Minimization for

Haiyang Li, Jigen Peng and Shigang Yue

Mathematical Problems in Engineering, 2015, vol. 2015, 1-6

Abstract:

The sparsity problems have attracted a great deal of attention in recent years, which aim to find the sparsest solution of a representation or an equation. In the paper, we mainly study the sparsity of underdetermined linear system via minimization for . We show, for a given underdetermined linear system of equations , that although it is not certain that the problem (i.e., subject to , where ) generates sparser solutions as the value of decreases and especially the problem generates sparser solutions than the problem (i.e., subject to ), there exists a sparse constant such that the following conclusions hold when : the problem generates sparser solution as the value of decreases; the sparsest optimal solution to the problem is unique under the sense of absolute value permutation; let and be the sparsest optimal solution to the problems and , respectively, and let not be the absolute value permutation of . Then there exist such that is the sparsest optimal solution to the problem and is the sparsest optimal solution to the problem .

Date: 2015
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2015/584712.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2015/584712.xml (text/xml)

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:hin:jnlmpe:584712

DOI: 10.1155/2015/584712

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().