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A multilinear singular value decomposition

by Lieven De Lathauwer, Bart De Moor, Joos Vandewalle - 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 higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order 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 higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc

I. SINGULAR VALUE DECOMPOSITION

by Andrew E. Yagle, A. Basics, U Is M M, V Is N N
"... 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

by Jody Hourigan, Lynn McIndoo - 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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. 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

by G. W. Stewart , 1992
"... This paper surveys the contributions of five mathematicians --- Eugenio Beltrami (1835--1899), Camille Jordan (1838--1921), James Joseph Sylvester (1814--1897), Erhard Schmidt (1876--1959), and Hermann Weyl (1885--1955) --- who were responsible for establishing the existence of the singular value de ..."
Abstract - Cited by 125 (1 self) - Add to MetaCart
This paper surveys the contributions of five mathematicians --- Eugenio Beltrami (1835--1899), Camille Jordan (1838--1921), James Joseph Sylvester (1814--1897), Erhard Schmidt (1876--1959), and Hermann Weyl (1885--1955) --- who were responsible for establishing the existence of the singular value

Generalized Singular Value Decomposition

by Cheonghee Park, Haesun Park
"... 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

by Lars Grasedyck, Lars Grasedyck - 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 ..."
Abstract - Cited by 178 (11 self) - Add to MetaCart
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

by Chi-jie Lu, Du-ming Tsai, Du-ming Tsai
"... Thin Film Transistor Liquid Crystal Displays (TFT-LCDs) 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

by D. C. Ross
"... An iterative algorithm for the singular value decomposition (SVD) of a non-zero m x n matrix M is described and illustrated numerically. Derivations of the algorithm and suf-ficient 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 non-zero m x n matrix M is described and illustrated numerically. Derivations of the algorithm and suf-ficient 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

by G. W. Stewart - 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 ..."
Abstract - Cited by 49 (0 self) - Add to MetaCart
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

by Shmuel Friedland , 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.
Results 1 - 10 of 13,214