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On the Uniqueness of Multilinear Decomposition of Nway arrays
, 2000
"... INTRODUCTION Consider an I # J matrix X and suppose that rank (X) = 3. Let x i,j denote the (i, j)th entry of X.Thenit holds that x i,j admits a threecomponent bilinear decomposition x i#j # # 3 f #1 a i#f b j#f #1# for all i = 1,...,I and j = 1,...,J. Equivalently, letting a f := [a 1,f ..."
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Cited by 100 (10 self)
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INTRODUCTION Consider an I # J matrix X and suppose that rank (X) = 3. Let x i,j denote the (i, j)th entry of X.Thenit holds that x i,j admits a threecomponent bilinear decomposition x i#j # # 3 f #1 a i#f b j#f #1# for all i = 1,...,I and j = 1,...,J. Equivalently, letting a f := [a 1,f ,...,a I,f ] T and similarly for b f , X # a 1 b T 1 # a 2 b T 2 # a 3 b T 3 #2# i
Tensor Decompositions and Applications
 SIAM REVIEW
, 2009
"... This survey provides an overview of higherorder tensor decompositions, their applications, and available software. A tensor is a multidimensional or N way array. Decompositions of higherorder tensors (i.e., N way arrays with N â¥ 3) have applications in psychometrics, chemometrics, signal proce ..."
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Cited by 722 (18 self)
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This survey provides an overview of higherorder tensor decompositions, their applications, and available software. A tensor is a multidimensional or N way array. Decompositions of higherorder tensors (i.e., N way arrays with N â¥ 3) have applications in psychometrics, chemometrics, signal
Generic and typical ranks of multiway arrays
 Linear Algebra Appl
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 28 (5 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
On the Eigenvectors of Real EvenOrder NWay Arrays in Sm,2
"... In this paper, we explore some inherent properties of two kinds of eigenvectors defined on real evenorder 2dimensional supersymmetric Nway arrays, and the main contribution is to show that any such Nway arrays has at least 2 linearly independent eigenvectors. ..."
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In this paper, we explore some inherent properties of two kinds of eigenvectors defined on real evenorder 2dimensional supersymmetric Nway arrays, and the main contribution is to show that any such Nway arrays has at least 2 linearly independent eigenvectors.
A ONEWAY ARRAY ALGORITHM FOR MATROID SCHEDULING
, 1991
"... The greedy algorithm is a standard paradigm for solving matroid optimization problems on sequential computers. This paper presents a greedy algorithm suitable for a fullypipelined linear array of processors, a generalization of Huang's algorithm [Hua90] for minimum spanning trees. Application ..."
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Cited by 2 (0 self)
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The greedy algorithm is a standard paradigm for solving matroid optimization problems on sequential computers. This paper presents a greedy algorithm suitable for a fullypipelined linear array of processors, a generalization of Huang's algorithm [Hua90] for minimum spanning trees. Application
Software pipelining: An effective scheduling technique for VLIW machines
, 1988
"... This paper shows that software pipelining is an effective and viable scheduling technique for VLIW processors. In software pipelining, iterations of a loop in the source program are continuously initiated at constant intervals, before the preceding iterations complete. The advantage of software pipe ..."
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Cited by 581 (3 self)
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pipelining is that optimal performance can be achieved with compact object code. This paper extends previous results of software pipelining in two ways: First, this paper shows that by using an improved algorithm, nearoptimal performance can be obtained without specialized hardware. Second, we propose a
Combining Branch Predictors
, 1993
"... One of the key factors determining computer performance is the degree to which the implementation can take advantage of instructionlevel parallelism. Perhaps the most critical limit to this parallelism is the presence of conditional branches that determine which instructions need to be executed ne ..."
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Cited by 630 (0 self)
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next. To increase parallelism, several authors have suggested ways of predicting the direction of conditional branches with hardware that uses the history of previous branches. The different proposed predictors take advantage of different observed patterns in branch behavior. This paper presents a
Some Numerical Results on the Rank of Generic ThreeWay Arrays over R
, 2009
"... Abstract. The aim of this paper is the introduction of a new method for the numerical computation of the rank of a threeway array, X ∈ RI×J×K, over R. We show that the rank of a threeway array over R is intimately related to the real solution set of a system of polynomial equations. Using this, we ..."
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Abstract. The aim of this paper is the introduction of a new method for the numerical computation of the rank of a threeway array, X ∈ RI×J×K, over R. We show that the rank of a threeway array over R is intimately related to the real solution set of a system of polynomial equations. Using this
Lowrank decomposition of multiway arrays: A signal processing perspective
 In IEEE SAM
, 2004
"... In many signal processing applications of linear algebra tools, the signal part of a postulated model lies in a socalled signal subspace, while the parameters of interest are in onetoone correspondence with a certain basis of this subspace. The signal subspace can often be reliably estimated from ..."
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Cited by 12 (0 self)
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from measured data, but the particular basis of interest cannot be identified without additional problemspecific structure. This is a manifestation of rotational indeterminacy, i.e., nonuniqueness of lowrank matrix decomposition. The situation is very different for three or higherway arrays, i
Generalizing the ColumnRow Matrix Decomposition to Multiway Arrays
"... In this paper, we provide two generalizations of the CUR matrix decomposition Y = CUR (also known as pseudoskeleton approximation method [1]) to the case of Nway arrays (tensors). These generalizations, which we called Fiber Sampling Tensor Decomposition types 1 and 2 (FSTD1 and FSTD2), provide ex ..."
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Cited by 14 (6 self)
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In this paper, we provide two generalizations of the CUR matrix decomposition Y = CUR (also known as pseudoskeleton approximation method [1]) to the case of Nway arrays (tensors). These generalizations, which we called Fiber Sampling Tensor Decomposition types 1 and 2 (FSTD1 and FSTD2), provide
Results 1  10
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679,439