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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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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
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
Realization of the Markov parameter sequences using the singular value decomposition of the Hankel matrix
, 1979
"... using the singular value decomposition of the ..."
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.
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
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
SINGULAR VALUE DECOMPOSITION GERˇSGORIN SETS
"... Abstract: In this note, we introduce the singular value decomposition Gerˇsgorin set, Γ SV (A), of an N × N complex matrix A, where N ≤ ∞. For N finite, the set Γ SV (A) is similar to the standard Gerˇsgorin set, Γ(A), in that it is a union of N closed disks in the complex plane and it contains the ..."
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Cited by 1 (1 self)
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Abstract: In this note, we introduce the singular value decomposition Gerˇsgorin set, Γ SV (A), of an N × N complex matrix A, where N ≤ ∞. For N finite, the set Γ SV (A) is similar to the standard Gerˇsgorin set, Γ(A), in that it is a union of N closed disks in the complex plane and it contains
Results 1  10
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155,201