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 language | English (US) |
|---|---|
| Pages (from-to) | 195-209 |
| Number of pages | 15 |
| Journal | Computational Statistics and Data Analysis |
| Volume | 41 |
| Issue number | 1 |
| DOIs | |
| State | Published - Nov 28 2002 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics
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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 journal › Article
TY - JOUR
T1 - A modified Gram-Schmidt-based downdating technique for ULV decompositions with applications to recursive TLS problems
AU - Erbay, Hasan
AU - Barlow, Jesse Louis
AU - Zhang, Zhenyue
PY - 2002/11/28
Y1 - 2002/11/28
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0037191701&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037191701&partnerID=8YFLogxK
U2 - 10.1016/S0167-9473(02)00069-5
DO - 10.1016/S0167-9473(02)00069-5
M3 - Article
AN - SCOPUS:0037191701
VL - 41
SP - 195
EP - 209
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
SN - 0167-9473
IS - 1
ER -