An efficient rank detection procedure for modifying the ULV decomposition

Yoon, Peter A.; Barlow, Jesse L.

doi:10.1007/bf02510414

Cited by 12 publications

(4 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The condition estimation used in these algorithms is inverse iteration (implemented in the Matlab function inviter), which allows us -for a fixed k -to restart the iterations in a simple way. The use of inverse iterations has also been suggested by Yoon and Barlow in connection with a ULV downdating algorithm [65]. The alternative ULV algorithm takes the following form for m n.…”

Section: Revealment: Determine An Orthogonalmentioning

confidence: 99%

Untitled

Fierro¹,

Hansen²,

Hansen³

1999

Numerical Algorithms

View full text Add to dashboard Cite

We describe a Matlab 5.2 package for computing and modifying certain rank-revealing decompositions that have found widespread use in signal processing and other applications. The package focuses on algorithms for URV and ULV decompositions, collectively known as UTV decompositions. We include algorithms for the ULLV decomposition, which generalizes the ULV decomposition to a pair of matrices. For completeness a few algorithms for computation of the RRQR decomposition are also included. The software in this package can be used as is, or can be considered as templates for specialized implementations on signal processors and similar dedicated hardware platforms.

show abstract

Section: Revealment: Determine An Orthogonalmentioning

confidence: 99%

Untitled

Fierro¹,

Hansen²,

Hansen³

1999

Numerical Algorithms

View full text Add to dashboard Cite

show abstract

“…Updating algorithms given by Stewart [14], Yoon and Barlow [1,15] and Barlow, Erbay and Zhang [3] append the new data to the bottom of the data matrix which makes them unsuitable for these applications. In this paper we present an O(n 2 ) updating algorithm which appends the new data to the top of matrix.…”

Section: Introductionmentioning

confidence: 99%

An Alternative Algorithm for a Sliding Window ULV Decomposition

Erbay

Barlow

2005

Computing

View full text Add to dashboard Cite

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 modi…ed much faster than the SVD.When modi…ying the ULVD, the accurate computation of the subspaces is required in certain time varying applications in signal processing. In this paper we present an updating algorithm which is suitable for large scaled matrices of low rank and as e¤ective as alternatives. The algorithm runs in O(n 2 ) time.

show abstract

“…However, if the decomposition must be modified by adding rows (updating) and/or deleting rows (downdating), then the SVD can be computationally expensive [13], whereas CODs may be updated and downdated in O(mn) flops [8,3,24,20,21]. Our algorithms for construction and refinement lead to a form that can be updated by any of these procedures.…”

mentioning

confidence: 99%

“…Here Φ(n) is a modestly growing function of n, say, √ n. This formulation is a variant of the one in [24,8,4]. We refer to k as the -pseudorank of X, corresponding to a definition used by Lawson and Hanson [16,p.…”

mentioning

confidence: 99%

An Alternative Algorithm for the Refinement of ULV Decompositions

Barlow

Erbay

Slapniucar

2005

SIAM J. Matrix Anal. & Appl.

Self Cite

View full text Add to dashboard Cite

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). It is useful in applications of the SVD such as principal components where we are interested in approximating a matrix by one of lower rank. It can be updated and downdated much more quickly than an SVD. In many instances, the ULVD must be refined to improve the approximation it gives for the important right singular subspaces or to improve the matrix approximation. Present algorithms to perform this refinement require O(mn) operations if the rank of the matrix is k, where k is very close to 0 or n, but these algorithms require O(mn 2 ) operations otherwise. Presented here is an alternative refinement algorithm that requires O(mn) operations no matter what the rank is. Our tests show that this new refinement algorithm produces similar improvement in matrix approximation and in the subspaces. We also propose slight improvements on the error bounds on subspaces and singular values computed by the ULVD.

show abstract

An efficient rank detection procedure for modifying the ULV decomposition

Cited by 12 publications

References 10 publications

Untitled

Untitled

An Alternative Algorithm for a Sliding Window ULV Decomposition

An Alternative Algorithm for the Refinement of ULV Decompositions

Contact Info

Product

Resources

About