An efficient rank detection procedure for modifying the ULV decomposition

Peter A. Yoon, Jesse L. Barlow

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The ULV decomposition (ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition (SVD). The problem of adding and deleting rows from the ULVD (called updating and downdating, respectively) is considered. The ULVD can be updated and downdated much faster than the SVD, hence its utility. When updating or downdating the ULVD, it is necessary to compute its numerical rank. In this paper, we propose an efficient algorithm which almost always maintains rank-revealing structure of the decomposition after an update or downdate without standard condition estimation. Moreover, we can monitor the accuracy of the information provided by the ULVD as compared to the SVD by tracking exact Frobenius norms of the two small blocks of the lower triangular factor in the decomposition.

Original languageEnglish (US)
Pages (from-to)781-801
Number of pages21
JournalBIT Numerical Mathematics
Volume38
Issue number4
DOIs
StatePublished - Dec 1998

Fingerprint

Singular value decomposition
Decompose
Updating
Frobenius norm
Orthogonal Decomposition
Triangular
Monitor
Efficient Algorithms
Update
Necessary

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

Cite this

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An efficient rank detection procedure for modifying the ULV decomposition. / Yoon, Peter A.; Barlow, Jesse L.

In: BIT Numerical Mathematics, Vol. 38, No. 4, 12.1998, p. 781-801.

Research output: Contribution to journalArticle

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