Robert E. Funderlic

Works (4)

Updated: July 5th, 2023 16:04

2003 article

Structured low rank approximation

Chu, M. T., Funderlic, R. E., & Plemmons, R. J. (2003, April 23). Linear Algebra and Its Applications, Vol. 366, pp. 157–172.

By: M. Chu n , R. Funderlic n & R. Plemmons*

Contributors: M. Chu n , R. Funderlic n & R. Plemmons*

author keywords: structured matrix; low rank approximation; optimization techniques; Toeplitz matrix
topics (OpenAlex): Statistical and numerical algorithms; Sparse and Compressive Sensing Techniques; Blind Source Separation Techniques
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)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2002 article

The Centroid Decomposition: Relationships between Discrete Variational Decompositions and SVDs

Chu, M. T., & Funderlic, R. E. (2002, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 23, pp. 1025–1044.

By: M. Chu*  & R. Funderlic*

Contributors: M. Chu*  & R. Funderlic*

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
topics (OpenAlex): Psychometric Methodologies and Testing; Sensory Analysis and Statistical Methods; Complex Network Analysis Techniques
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 article

Rank Modifications of Semidefinite Matrices Associated with a Secant Update Formula

Chu, M. T., Funderlic, R. E., & Golub, G. H. (1998, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 20, pp. 428–436.

By: M. Chu* , R. Funderlic* & G. Golub

Contributors: M. Chu* , R. Funderlic* & G. Golub

author keywords: rank-one reduction; Wedderburn theorem; BFGS update; DFP update; quasi-Newton methods; rank subtractivity; rank additivity
topics (OpenAlex): Matrix Theory and Algorithms; Advanced Optimization Algorithms Research; Sparse and Compressive Sensing Techniques
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 article

On a Variational Formulation of the Generalized Singular Value Decomposition

Chu, M. T., Funderlic, R. E., & Golub, G. H. (1997, October 1). SIAM Journal on Matrix Analysis and Applications, Vol. 18, pp. 1082–1092.

By: M. Chu* , R. Funderlic* & G. Golub

Contributors: M. Chu* , R. Funderlic* & G. Golub

author keywords: generalized eigenvalue and eigenvector; generalized singular value and singular vector; stationary value and stationary point; deflation; duality
topics (OpenAlex): Matrix Theory and Algorithms; Elasticity and Material Modeling
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

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