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

Authors:
Hasan Erbay;Jesse L. Barlow;Zhenyue Zhang
Affiliations:
Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA 16802-6106, USA;Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA 16802-6106, USA;Department of Mathematics, Zhejiang University, Hangzhou 310027, People's Republic of China
Venue:
Computational Statistics & Data Analysis
Year:
2002

Citing 6
Cited 1

Updating a rank-revealing ULV decomposition

SIAM Journal on Matrix Analysis and Applications
Downdating the Singular Value Decomposition

SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
Total least squares algorithms based on rank-revealing complete orthogonal decompositions

Proceedings of the second international workshop on Recent advances in total least squares techniques and errors-in-variables modeling
Solving recursive TLS problems using the rank-revealing ULV decomposition

Proceedings of the second international workshop on Recent advances in total least squares techniques and errors-in-variables modeling
Modifying two-sided orthogonal decompositions: algorithms, implementation, and applications

Modifying two-sided orthogonal decompositions: algorithms, implementation, and applications

An efficient algorithm for rank and subspace tracking

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.03

Visualization

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.