Works (4)
Updated: July 5th, 2023 16:04
2003 journal article
Structured low rank approximation
LINEAR ALGEBRA AND ITS APPLICATIONS, 366(SPEC. ISS.), 157–172.
Contributors: M. Chu n , n & R. Plemmons*
author keywords: structured matrix; low rank approximation; optimization techniques; Toeplitz matrix
TL;DR:
Two procedures for constructing the nearest structured low rank matrix are proposed and are flexible enough that they can be applied to any lower rank, any linear structure, and any matrix norm in the measurement of nearness.
(via Semantic Scholar)
open access via doi.org (publisher)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2002 journal article
The centroid decomposition: Relationships between discrete variational decompositions and SVDs
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 23(4), 1025–1044.
Contributors: M. Chu* & *
author keywords: data matrix; loading matrix; scoring matrix; indexing matrix; factor analysis; centroid method; singular value decomposition; low rank approximation; semidiscrete decomposition; centroid decomposition; low rank decompositions; integer programming
TL;DR:
One major purpose of this work is to show fundamental relationships between the singular value, centroid, and semidiscrete decompositions, which unifies an entire class of truncated SVD approximations.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
1998 journal article
Rank modifications of semidefinite matrices associated with a secant update formula
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 20(2), 428–436.
Contributors: M. Chu* , * & G. Golub
author keywords: rank-one reduction; Wedderburn theorem; BFGS update; DFP update; quasi-Newton methods; rank subtractivity; rank additivity
TL;DR:
This paper analyzes rank modification of symmetric positive definite matrices H of the form H + P, where H −M denotes a step of reducing H to a lower-rank, symmetric and positive semidefinite matrix and (H −M) + P denotes astep of restoring H−M to a symmetricpositive definite matrix.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
1997 journal article
On a variational formulation of the generalized singular value decomposition
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 18(4), 1082–1092.
Contributors: M. Chu* , * & G. Golub
author keywords: generalized eigenvalue and eigenvector; generalized singular value and singular vector; stationary value and stationary point; deflation; duality
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
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