A modified Gram-Schmidt-based downdating technique for ULV decompositions with applications to recursive TLS problems

Hasan Erbay, Jesse Louis Barlow, Zhenyue Zhang

Research output: Contribution to journalArticle

10 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 ULVD can be updated and downdated much faster than the SVD, hence its utility in the solution of recursive total least squares (TLS) problems. However, the robust implementation of ULVD after the addition and deletion of rows (called updating and downdating, respectively) is not altogether straightforward. When updating or downdating the ULVD, the accurate computation of the subspaces necessary to solve the TLS problem is of great importance. In this paper, algorithms are given to compute simple parameters that can often show when good subspaces have been computed.

Original languageEnglish (US)
Pages (from-to)195-209
Number of pages15
JournalComputational Statistics and Data Analysis
Volume41
Issue number1
DOIs
StatePublished - Nov 28 2002

Fingerprint

Total Least Squares
Least Squares Problem
Singular value decomposition
Decompose
Updating
Subspace
Orthogonal Decomposition
Deletion
Necessary

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

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A modified Gram-Schmidt-based downdating technique for ULV decompositions with applications to recursive TLS problems. / Erbay, Hasan; Barlow, Jesse Louis; Zhang, Zhenyue.

In: Computational Statistics and Data Analysis, Vol. 41, No. 1, 28.11.2002, p. 195-209.

Research output: Contribution to journalArticle

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