An efficient algorithm for rank and subspace tracking

Authors:
Hasan Erbay
Affiliations:
Department of Mathematics,Kırıkkale University, Yahşihan,Kırıkkale, 71100, Turkey
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2006

Citing 9
Cited 0

Updating a rank-revealing ULV decomposition

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Bounding the Subspaces from Rank Revealing Two-Sided Orthogonal Decompositions

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Downdating the Singular Value Decomposition

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Total least squares algorithms based on rank-revealing complete orthogonal decompositions

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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
An Alternative Algorithm for the Refinement of ULV Decompositions

SIAM Journal on Matrix Analysis and Applications
Fast, rank adaptive subspace tracking and applications

IEEE Transactions on Signal Processing
An updating algorithm for subspace tracking

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

Computational Statistics & Data Analysis

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Abstract

Traditionally, the singular value decomposition (SVD) has been used in rank and subspace tracking methods. However, the SVD is computationally costly, especially when the problem is recursive in nature and the size of the matrix is large. The truncated ULV decomposition (TULV) is an alternative to the SVD. It provides a good approximation to subspaces for the data matrix and can be modified quickly to reflect changes in the data. It also reveals the rank of the matrix. This paper presents a TULV updating algorithm. The algorithm is most efficient when the matrix is of low rank. Numerical results are presented that illustrate the accuracy of the algorithm.