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8,735
A multilinear singular value decomposition
 SIAM J. Matrix Anal. Appl
, 2000
"... Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc., are ..."
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Cited by 472 (22 self)
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Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
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Cited by 555 (22 self)
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toimplement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank. The algorithm is iterative and produces a sequence of matrices {X k, Y k} and at each step, mainly performs a softthresholding operation on the singular values of the matrix Y k. There are two
The Complex Structures Singular Value
, 1993
"... A tutorial introduction to the complex structured singular value (µ) is presented, with an emphasis on the mathematical aspects of µ. The µbased methods discussed here have been useful for analyzing the performance and robustness properties of linear feedback systems. Several tests ..."
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Cited by 192 (14 self)
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A tutorial introduction to the complex structured singular value (µ) is presented, with an emphasis on the mathematical aspects of µ. The µbased methods discussed here have been useful for analyzing the performance and robustness properties of linear feedback systems. Several tests
Accurate Singular Values of Bidiagonal Matrices
 SIAM J. SCI. STAT. COMPUT
, 1990
"... Computing the singular values of a bidiagonal matrix is the fin al phase of the standard algow rithm for the singular value decomposition of a general matrix. We present a new algorithm hich computes all the singular values of a bidiagonal matrix to high relative accuracy independent of their magni ..."
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Cited by 129 (18 self)
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Computing the singular values of a bidiagonal matrix is the fin al phase of the standard algow rithm for the singular value decomposition of a general matrix. We present a new algorithm hich computes all the singular values of a bidiagonal matrix to high relative accuracy independent
Singularvalue
"... decomposition analysis of source illumination in seismic interferometry by multidimensional deconvolution ..."
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decomposition analysis of source illumination in seismic interferometry by multidimensional deconvolution
Hierarchical singular value decomposition of tensors
 SIAM Journal on Matrix Analysis and Applications
"... Abstract. We define the hierarchical singular value decomposition (SVD) for tensors of order d ≥ 2. This hierarchical SVD has properties like the matrix SVD (and collapses to the SVD in d = 2), and we prove these. In particular, one can find low rank (almost) best approximations in a hierarchical fo ..."
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Cited by 178 (11 self)
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Abstract. We define the hierarchical singular value decomposition (SVD) for tensors of order d ≥ 2. This hierarchical SVD has properties like the matrix SVD (and collapses to the SVD in d = 2), and we prove these. In particular, one can find low rank (almost) best approximations in a hierarchical
On the Early History of the Singular Value Decomposition
, 1992
"... This paper surveys the contributions of five mathematicians  Eugenio Beltrami (18351899), Camille Jordan (18381921), James Joseph Sylvester (18141897), Erhard Schmidt (18761959), and Hermann Weyl (18851955)  who were responsible for establishing the existence of the singular value de ..."
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Cited by 125 (1 self)
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This paper surveys the contributions of five mathematicians  Eugenio Beltrami (18351899), Camille Jordan (18381921), James Joseph Sylvester (18141897), Erhard Schmidt (18761959), and Hermann Weyl (18851955)  who were responsible for establishing the existence of the singular value
MAXPLUS SINGULAR VALUES
, 2014
"... In this paper we prove a new characterization of the maxplus singular values of a maxplus matrix, as the maxplus eigenvalues of an associated maxplus matrix pencil. This new characterization allows us to compute maxplus singular values quickly and accurately. As well as capturing the asymptotic ..."
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In this paper we prove a new characterization of the maxplus singular values of a maxplus matrix, as the maxplus eigenvalues of an associated maxplus matrix pencil. This new characterization allows us to compute maxplus singular values quickly and accurately. As well as capturing
SINGULAR VALUES OF TOURNAMENT MATRICES
, 1999
"... Upper and lower bounds on both the largest and smallest singular values of a tournament matrix M of order n are obtained. For most values of n, the matrices M for which equality holds are characterized. ..."
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Cited by 2 (0 self)
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Upper and lower bounds on both the largest and smallest singular values of a tournament matrix M of order n are obtained. For most values of n, the matrices M for which equality holds are characterized.
The Singular Value Decomposition
 College of the Redwoods. 16 Dec. 2005 http://online.redwoods.cc.ca.us/instruct/darnold/ LAPROJ/Fall98/JodLynn/report2.pdf
, 1998
"... . We explore the derivation of the SVD and its role in digital image processing. By using MATLAB, we will demonstrate how the SVD is used to minimize the size needed to store an image. Introduction The singular value decomposition is a highlight of linear algebra. It plays an interesting, fundamen ..."
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Cited by 4 (0 self)
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. We explore the derivation of the SVD and its role in digital image processing. By using MATLAB, we will demonstrate how the SVD is used to minimize the size needed to store an image. Introduction The singular value decomposition is a highlight of linear algebra. It plays an interesting
Results 1  10
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8,735