Improved bound for rank revealing LU factorizations

Tsung Min Hwang, Wen Wei Lin, Daniel Pierce

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In many applications it is necessary to determine the rank (or numerical rank) of a matrix. Many of these situations involve matrices that are very large order or that are sparse or that may undergo some form of modification (rank-k update, row or column appended or removed). In these cases the singular value decomposition's cost may be prohibitively high or the decomposition may not be computationally feasible (especially for large sparse problems). We thus examine the theoretical merits of rank revealing LU (RRLU) factorizations. We find that in those cases where the nullity is small and the gap is well defined, an RRLU factorization could be a very useful tool.

Original languageEnglish
Pages (from-to)173-186
Number of pages14
JournalLinear Algebra and Its Applications
Volume261
Issue number1-3
DOIs
Publication statusPublished - 1997 Aug

Fingerprint

LU Factorization
Factorization
Singular value decomposition
Nullity
Well-defined
Costs
Update
Rank of a matrix
Decompose
Necessary

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

Cite this

Improved bound for rank revealing LU factorizations. / Hwang, Tsung Min; Lin, Wen Wei; Pierce, Daniel.

In: Linear Algebra and Its Applications, Vol. 261, No. 1-3, 08.1997, p. 173-186.

Research output: Contribution to journalArticle

Hwang, Tsung Min ; Lin, Wen Wei ; Pierce, Daniel. / Improved bound for rank revealing LU factorizations. In: Linear Algebra and Its Applications. 1997 ; Vol. 261, No. 1-3. pp. 173-186.
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