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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 467 (20 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
I. SINGULAR VALUE DECOMPOSITION
"... Abstract — We review the basic results on: (1) the singular value decomposition (SVD); (2) sensitivity and conditioning of solutions of linear systems of equations; (3) regularization; and (4) iterative solution of linear systems of equations. These are applied to the specific problem of computing a ..."
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Abstract — We review the basic results on: (1) the singular value decomposition (SVD); (2) sensitivity and conditioning of solutions of linear systems of equations; (3) regularization; and (4) iterative solution of linear systems of equations. These are applied to the specific problem of computing
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
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 122 (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
Generalized Singular Value Decomposition
"... In Linear Discriminant Analysis (LDA), a dimension reducing linear transformation is found in order to better distinguish clusters from each other in the reduced dimensional space. However, LDA has a limitation that one of the scatter matrices is required to be nonsingular and the nonlinearly cluste ..."
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clustered structure is not easily captured. We propose a nonlinear discriminant analysis based on kernel functions and the generalized singular value decomposition called KDA/GSVD, which is a nonlinear extension of LDA and works regardless of the nonsingularity of the scatter matrices in either the input
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 177 (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
Singular Value Decomposition
"... Thin Film Transistor Liquid Crystal Displays (TFTLCDs) have become increasingly popular and dominant as display devices. Surface defects on TFT panels not only cause visual failure, but result in electrical failure and loss of LCD operational functionally. In this paper, we propose a global approac ..."
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of textures. It is based on a global image reconstruction scheme using the singular value decomposition (SVD). Taking the image as a matrix of pixels, the singular values on the decomposed diagonal matrix represent different degrees of detail in the textured image. By selecting the proper singular values
Algorithm for singular value decomposition
"... An iterative algorithm for the singular value decomposition (SVD) of a nonzero m x n matrix M is described and illustrated numerically. Derivations of the algorithm and sufficient conditions for convergence are outlined. SVD is one of the most important procedures in digital processing of signals ..."
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An iterative algorithm for the singular value decomposition (SVD) of a nonzero m x n matrix M is described and illustrated numerically. Derivations of the algorithm and sufficient conditions for convergence are outlined. SVD is one of the most important procedures in digital processing of signals
Perturbation Theory for the Singular Value Decomposition
 IN SVD AND SIGNAL PROCESSING, II: ALGORITHMS, ANALYSIS AND APPLICATIONS
, 1990
"... The singular value decomposition has a number of applications in digital signal processing. However, the the decomposition must be computed from a matrix consisting of both signal and noise. It is therefore important to be able to assess the effects of the noise on the singular values and singular v ..."
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Cited by 49 (0 self)
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The singular value decomposition has a number of applications in digital signal processing. However, the the decomposition must be computed from a matrix consisting of both signal and noise. It is therefore important to be able to assess the effects of the noise on the singular values and singular
SINGULAR VALUE DECOMPOSITION IN DNA MICROARRAYS
, 2004
"... We show that the singular value decomposition with respect to a certain inner product in R M gives the generalized singular value decomposition for two matrices with M columns and different sizes of rows, introduced recently to compare two sets of DNA microarrays of different organisms. ..."
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We show that the singular value decomposition with respect to a certain inner product in R M gives the generalized singular value decomposition for two matrices with M columns and different sizes of rows, introduced recently to compare two sets of DNA microarrays of different organisms.
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936,048