Готові списки джерел за темами / Kronecker products

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Добірка наукової літератури з теми "Kronecker products"

Автор: Grafiati
Опубліковано: 4 червня 2021
Оновлено: 27 липня 2024

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Статті в журналах з теми "Kronecker products"

1

Pak, Igor, and Greta Panova. "Unimodality via Kronecker products." Journal of Algebraic Combinatorics 40, no. 4 (April 5, 2014): 1103–20. http://dx.doi.org/10.1007/s10801-014-0520-y.

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2

Zhang, Huamin, and Feng Ding. "On the Kronecker Products and Their Applications." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/296185.

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This paper studies the properties of the Kronecker product related to the mixed matrix products, the vector operator, and the vec-permutation matrix and gives several theorems and their proofs. In addition, we establish the relations between the singular values of two matrices and their Kronecker product and the relations between the determinant, the trace, the rank, and the polynomial matrix of the Kronecker products.
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3

Watts, Valerie L. "Boolean rank of Kronecker products." Linear Algebra and its Applications 336, no. 1-3 (October 2001): 261–64. http://dx.doi.org/10.1016/s0024-3795(01)00338-x.

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4

Brown, Andrew, Stephanie van Willigenburg, and Mike Zabrocki. "Expressions for Catalan Kronecker products." Pacific Journal of Mathematics 248, no. 1 (October 1, 2010): 31–48. http://dx.doi.org/10.2140/pjm.2010.248.31.

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5

Zhao, Hui, Jiuqiang Han, Naiyan Wang, Congfu Xu, and Zhihua Zhang. "A Fast Spectral Relaxation Approach to Matrix Completion via Kronecker Products." Proceedings of the AAAI Conference on Artificial Intelligence 25, no. 1 (August 4, 2011): 580–85. http://dx.doi.org/10.1609/aaai.v25i1.7913.

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In the existing methods for solving matrix completion, such as singular value thresholding (SVT), soft-impute and fixed point continuation (FPCA) algorithms, it is typically required to repeatedly implement singular value decompositions (SVD) of matrices.When the size of the matrix in question is large, the computational complexity of finding a solution is costly. To reduce this expensive computational complexity, we apply Kronecker products to handle the matrix completion problem. In particular, we propose using Kronecker factorization, which approximates a matrix by the Kronecker product of several matrices of smaller sizes. Weintroduce Kronecker factorization into the soft-impute framework and devise an effective matrix completion algorithm.Especially when the factorized matrices have about the samesizes, the computational complexity of our algorithm is improved substantially.
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6

Pollock, D. Stephen G. "Multidimensional Arrays, Indices and Kronecker Products." Econometrics 9, no. 2 (April 28, 2021): 18. http://dx.doi.org/10.3390/econometrics9020018.

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Much of the algebra that is associated with the Kronecker product of matrices has been rendered in the conventional notation of matrix algebra, which conceals the essential structures of the objects of the analysis. This makes it difficult to establish even the most salient of the results. The problems can be greatly alleviated by adopting an orderly index notation that reveals these structures. This claim is demonstrated by considering a problem that several authors have already addressed without producing a widely accepted solution.
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7

Özel, Mustafa. "Schur Complements of Block Kronecker Products." Deu Muhendislik Fakultesi Fen ve Muhendislik 19, no. 57 (January 1, 2017): 845–50. http://dx.doi.org/10.21205/deufmd.2017195774.

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8

Liu, Jian. "SPECTRAL RADIUS, KRONECKER PRODUCTS AND STATIONARITY." Journal of Time Series Analysis 13, no. 4 (July 1992): 319–25. http://dx.doi.org/10.1111/j.1467-9892.1992.tb00110.x.

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9

Allen, Jeffery C. "Matrix Expansion by Orthogonal Kronecker Products." American Mathematical Monthly 102, no. 6 (June 1995): 538. http://dx.doi.org/10.2307/2974769.

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10

Liechty, Merrill W., and Matthew Tibbits. "Multivariate sufficient statistics using Kronecker products." Statistics and Computing 20, no. 3 (April 23, 2009): 335–41. http://dx.doi.org/10.1007/s11222-009-9127-x.

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Дисертації з теми "Kronecker products"

1

Broxson, Bobbi Jo. "The Kronecker Product." UNF Digital Commons, 2006. http://digitalcommons.unf.edu/etd/25.

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This paper presents a detailed discussion of the Kronecker product of matrices. It begins with the definition and some basic properties of the Kronecker product. Statements will be proven that reveal information concerning the eigenvalues, singular values, rank, trace, and determinant of the Kronecker product of two matrices. The Kronecker product will then be employed to solve linear matrix equations. An investigation of the commutativity of the Kronecker product will be carried out using permutation matrices. The Jordan - Canonical form of a Kronecker product will be examined. Variations such as the Kronecker sum and generalized Kronecker product will be introduced. The paper concludes with an application of the Kronecker product to large least squares approximations.
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2

Gilliam, Paul John. "A practical parallel algorithm for the minimization of Krönecker Reed-Muller expansions." PDXScholar, 1991. https://pdxscholar.library.pdx.edu/open_access_etds/4178.

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A number of recent developments has increased the desirability of using exclusive OR (XOR) gates in the synthesis of switching functions. This has, in turn, led naturally to an increased interest in algorithms for the minimization of Exclusive-Or Sum of Products (ESOP) forms. Although this is an active area of research, it is not nearly as developed as the traditional Sum of Products forms. Computer programs to find minimum ESOPs are not readily available and those that do exist are impractical to use as investigative tools because they are too slow and/or require too much memory. A practical tool would be easy enough to use (faster/smaller) so that it could be run many times to explore the solution space of the minimization problem as well as to provide a baseline of comparison. This thesis develops and investigates such a tool.
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3

Zeng, Xiaoqiang. "Minimization of Generalized Reed-Muller Expansion and Its Sub-class." PDXScholar, 1994. https://pdxscholar.library.pdx.edu/open_access_etds/4991.

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Several classes of AND-EXOR circuit expressions have been defined and their relationship have been shown. A new class of AND-EXOR circuit, the Partially Mixed Polarity Reed-Muller Expression(PMPRM), which is a subclass of the Generalized Reed-Muller expression, is created, along with an efficient minimization algorithm. This new AND/EXOR circuit form has the following features: • Since this sub-family of ESOP (with a total of n2n-I22n-i - (n-1)2n forms which includes the 2n Fixed-Polarity Reed-Muller forms) is much larger than the Kronecker Reed-Muller(KRM) expansion(with 3n forms), generally the minimal form of this expansion will be much closer to the minimal ESOP than the minimal form of KRM expansion. • It is a sub-class of the Generalized Reed-Muller Expansion, thus has better testibility than other AND/EXOR circuits. Those design methods of easily testable GRM circuit networks[ 6] [35] can also be used for this new circuit form. • The exact solution to the minimization of this new expansion provides a upperbound for the minimization of ORM expansion. In this thesis, we prove that to calculate a PMPRM expansion from one of its adjacent polarity expansion , only one EXOR operation is needed. By calculating the adjacent polarity expansions one-by-one and searching all the PMPRM forms the minimum one can be found. A speedup approach allows us to find the exact minimum PMPRM without calculating all forms. The algorithm is explained by minimizing the 3-variable functions and is demonstrated by flow graphs. With the introduction of termwise complementary expansion diagram, a computerized algorithm for the calculation of any ORM expansion is presented. The exact minimum ORM form can be obtained by an exhaustive search through all ORM forms. A heuristic minimization algorithm, which is designed to decrease the time complexity of the exact one, is also presented in this thesis. Instead of depending on the number of input variables, the computation time of this quasi-minimum algorithm depends mainly on the complexity of the input functions, thus can solve much larger problems. The exact minimization algorithm for PMPRM and the quasi-minimum ORM minimization algorithm have been implemented in C programs and a set of benchmark functions has been tested. The results are compared to those from [16], [36], and Espresso's. In most cases our program gives the same or better solutions.
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4

Liang, Dong Cowles Mary Kathryn. "Issues in Bayesian Gaussian Markov random field models with application to intersensor calibration." Iowa City : University of Iowa, 2009. http://ir.uiowa.edu/etd/400.

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5

Wang, Wei. "Estimation Approaches of Sufficient Reduction under Kronecker Product Structure." Thesis, The George Washington University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10744337.

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We propose methods to estimate linear combinations of several predictors that are measured repeatedly over time, that contain sufficient information for the regression of the predictors on the outcome. We assume that the first moments of the predictors can be decomposed into a time and a marker component via a Kronecker product structure that accommodates the longitudinal nature of the predictors. We then extend least squares and model-based sufficient dimension reduction techniques to accommodate this setting. We derive some analytic properties, and we compare the performance of the various approaches under different assumptions on the structure of the predictors in simulations.

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6

Badahmane, Achraf. "Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres." Thesis, Littoral, 2019. http://www.theses.fr/2019DUNK0543.

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La résolution numérique des problèmes de point-selle a eu une attention particulière ces dernières années. À titre d'exemple, la mécanique des fluides et solides conduit souvent à des problèmes de point-selle. Ces problèmes se présentent généralement par des équations aux dérivées partielles que nous linéarisons et discrétisons. Le problème linéaire obtenu est souvent mal conditionné. Le résoudre par des méthodes itératives standard n'est donc pas approprié. En plus, lorsque la taille du problème est grande, il est nécessaire de procéder par des méthodes de projections. Nous nous intéressons dans ce sujet de thèse à développer des méthodes numériques robustes et efficaces de résolution numérique de problèmes de point-selle. Nous appliquons les méthodes de Krylov avec des techniques de préconditionnement bien adaptées à la résolution de problème de point selle. L'efficacité de ces méthodes dans les tests numériques
In these last years there has been a surge of interest in saddle point problems. For example, the mechanics of fluids and solids often lead to saddle point problems. These problems are usually presented by partial differential equations that we linearize and discretize. The linear problem obtained is often ill-conditioned. Solving it by standard iterative methods is not appropriate. In addition, when the size of the problem is large, it is necessary to use the projection methods. We are interested in this thesis topic to develop an efficient numerical methods for solving saddle point problems. We apply the Krylov subspace methods incorporated with suitable preconditioners for solving these types of problems. The effectiveness of these methods is illustrated by the numerical experiments
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7

Ben, Hadj Braiek Ennaceur. "Application des fonctions de Walsh et des fonctions modulatrices à la modélisation des systèmes continus non linéaires." Lille 1, 1990. http://www.theses.fr/1990LIL10072.

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La modélisation d'un processus recouvre deux aspects : le choix d'un modèle mathématique, et la détermination de ses paramètres. Différents modèles de systèmes continus sont présentés, et le produit de Kronecker est introduit pour formaliser simplement des équations différentielles non linéaires multivariables, que ce soit des équations d'état ou relations différentielles entrées/sorties. La détermination des paramètres de ces modèles est ensuite considérée par l'utilisation des fonctions de Walsh et des fonctions modulatrices. Plusieurs algorithmes sont proposés et implantés sous la forme d'un logiciel d'identification : logid. Ces méthodes ont été validées sur des exemples concrets d'identification de paramètres et de simplification de modèles. Une procédure de réduction de dimensionalité utilisant les fonctions orthogonales a également été proposée
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8

Koroko, Abdoulaye. "Natural gradient-based optimization methods for deep neural networks." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG068.

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La méthode du gradient stochastique est la technologie actuellement prédominante pour effectuer la phase d'entraînement des réseaux de neurones. Par rapport à une descente classique, le calcul du vrai gradient comme une moyenne sur les données est remplacé par un élément aléatoire de la somme. En présence de données massives, cette approximation audacieuse permet de diminuer le nombre d'évaluations de gradients élémentaires et d'alléger le coût de chaque itération. Le prix à payer est l'apparition d'oscillations et la lenteur de convergence souvent excessive en nombre d'itérations. L'objectif de cette thèse est de concevoir une approche à la fois : (i) plus robuste, en faisant appel aux méthodes fondamentales qui ont fait leur preuve en optimisation classique, i.e., en dehors du cadre de l'apprentissage ; et (ii) plus rapide, en termes de vitesse convergence. Nous nous intéressons en particulier aux méthodes de second ordre, connues pour leur stabilité et leur rapidité de convergence. Pour éviter le goulot d'étranglement de ces méthodes, qui est le coût exorbitant d'une itération où intervient un système linéaire à matrice pleine, nous tentons d'améliorer une approximation récemment introduite sous le nom de Kronecker-Factorized Approximation of Curvature (KFAC) pour la matrice de Fisher, laquelle remplace la matrice hessienne dans ce contexte. Plus précisément, nos axes de travail sont : (i) construire de nouvelles factorisations de Kronecker fondées sur une justification mathématique plus rigoureuse que KFAC ; (ii) prendre en compte l'information issue des blocs hors diagonaux de la matrice de Fisher, qui représentent l'interaction entre les différentes couches ; (iii) généraliser KFAC à une architecture de réseau autre que celles pour lesquelles elle a été initialement développée
The stochastic gradient method is currently the prevailing technology for training neural networks. Compared to a classical descent, the calculation of the true gradient as an average over the data is replaced by a random element of the sum. When dealing with massive data, this bold approximation enables one to decrease the number of elementary gradient evaluations and to alleviate the cost of each iteration. The price to be paid is the appearance of oscillations and the slowness of convergence, which is often excessive in terms of number of iterations. The aim of this thesis is to design an approach that is both: (i) more robust, using the fundamental methods that have been successfully proven in classical optimization, i.e., outside the learning framework; and (ii) faster in terms of convergence speed. We are especially interested in second-order methods, known for their stability and speed of convergence. To circumvent the bottleneck of these methods, which lies in the prohibitive cost of an iteration involving a linear system with a full matrix, we attempt to improve an approximation recently introduced as Kronecker-Factorized Approximation of Curvature (KFAC) for the Fisher matrix, which replaces the Hessian matrix in this context. More specifically, our work focuses on: (i) building new Kronecker factorizations based on a more rigorous mathematical justification than in KFAC; (ii) taking into account the information from the off-diagonal blocks of the Fisher matrix, which represent the interaction between the different layers; (iii) generalizing KFAC to a network architecture other than those for which it had been initially developed
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9

Luu, Ba Thang. "Matrix-based implicit representations of algebraic curves and surfaces and applications." Nice, 2011. http://www.theses.fr/2011NICE4035.

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Dans cette thèse, nous introduisons et étudions une nouvelle représentation implicite des hypersurfaces rationnelles plongées dans un espace projectif de dimension arbitraire. Nous illustrons les avantages de cette représentation matricielle en abordant plusieurs problèmes importants intervenant en conception géométrique assistée par ordinateur : les problèmes d’intersection entre deux courbes, entre une courbe et une surface ou bien encore entre deux surfaces, le problème d’appartenance d’une point à une courbe ou une surface, le problème du calcul de la pré-image d’un point donné par une paramétrisation et enfin le problème du calcul des singularités d’une courbe rationnelle. L’approche développée dans ce travail de thèse est basée sur la combinaison de méthodes symboliques et numériques. En effet, une première étape symbolique consiste à transformer le problème considéré en un réseau de matrices. La deuxième étape consiste alors à calculer les valeurs propres généralisées de ce pinceau à l’aide de méthodes numériques. Pour cela, un algorithme d’extraction de la partie régulière d’un pinceau univarié, respectivement bivarié, de matrices non carrées est présenté. Une implémentation de ces travaux dans les systèmes de calcul formel Mathemagix et Maple est présentée en appendice. Le dernier chapitre est consacré » à un algorithme qui, étant donné un ensemble de polynômes univariés ∱₁,…∱s construit un ensemble de polynômes U₁,…, Us dont les degrés sont prescrits, tels que le degré du pgcd (∱₁ + U₁,…, ∱s + Us) est supérieur ou égal à un entier donné sous des hypothèses de généricité
In this thesis, we introduce and study a new implicit representation of rational curves of arbitrary dimensions and propose an implicit representation of rational hypersurfaces. The, we illustrate the advantages of this matrix representation by addressing several important problems of Computer Aided Geometric Design (CAGD) : the curve/curve, curve/surface and surface/surface intersection problems, the point-on-curve and inversion problems, the computation of singularities of rational curves. We also develop some symbolic/numeric algorithms to manipulate these new representations for example : the algorithm for extracting the regular part of a non square pencil of univariate polynomial matrices and bivariate polynomial matrices. In the appendix of this thesis work we present an implementation of these methods in the computeur algebra systems Mathemagix and Maple. In th last chapter, we describe an algorithm which, given a set of univariate polynomials ∱₁,…∱s returns a set of polynomials U₁,…, Us with prescribed degree-bounds such that the degree of gcd (∱₁ + U₁,…, ∱s + Us) is bounded below by a given degree assuming some genericity hypothesis
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10

Abouir, Jilali. "Problèmes concernant l'approximation rationnelle à plusieurs variables." Lille 1, 1992. http://www.theses.fr/1992LIL10054.

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Dans le cadre de l'interpolation rationnelle à plusieurs variables, nous étudions les propriétés fondamentales suivantes: continuité de l'opérateur d'approximation, les conditions nécessaires et suffisantes pour avoir la normalité de l'approximant de Newton-Pade. Dans la seconde partie, nous étudions une extension du théorème de Kronecker au cas de séries entières à deux variables, nous faisons la liaison avec les approximants de Pade homogènes. Dans la troisième partie, nous définissons les approximants de Pade homogènes. Dans la troisième partie, nous définissons les approximants de Newton-Pade partiel et les approximants de type Newton-Pade au cas de plusieurs variables, c'est une généralisation du cas scalaire introduit par C. Brezinski. L'avantage de ces approximants est l'utilisation des renseignements sur les zéros et les pôles d'une fonction f développable en série formelle, pour améliorer l'approximation. Dans la quatrième partie, nous donnons deux approches sur la formulation de l'erreur de l'interpolation rationnelle et de l'approximation de Pade à plusieurs variables
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Книги з теми "Kronecker products"

1

Loan, Charles F. Van. Approximation with Kronecker products. Ithaca, N.Y: Cornell Theory Center, Cornell University, 1992.

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2

Steeb, W. H. Kronecker product of matrices and applications. Mannheim: B.I. Wissenschaftsverlag, 1991.

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3

Dayar, Tuğrul. Analyzing Markov Chains using Kronecker Products. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4190-8.

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4

Dayar, Tuğrul. Analyzing Markov Chains using Kronecker Products: Theory and Applications. New York, NY: Springer New York, 2012.

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5

Blasiak, Jonah. Geometric complexity theory IV: Nonstandard quantum group for the Kronecker problem. Providence, Rhode Island: American Mathematical Society, 2015.

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6

1976-, Hardy Yorick, ed. Matrix calculus and Kronecker product: A practical approach to linear and multilinear algebra. 2nd ed. Singapore: World Scientific, 2011.

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7

Kiat, Shi Tan, ed. Matrix calculus and Kronecker product with applications and C++ programs. Singapore: World Scientific, 1997.

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8

Beelen, Theodorus Gertrudis Jospeh. New algorithms for computing the Kronecker structure of a pencil with applications to systems and control theory. [Eindhoven?]: T.G.J. Beelen, 1987.

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9

Graham, Alexander. Kronecker Products and Matrix Calculus with Applications. Dover Publications, Incorporated, 2018.

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10

Graham, Alexander. Kronecker Products and Matrix Calculus With Applications. Ellis Horwood Ltd, 1986.

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Частини книг з теми "Kronecker products"

1

Dayar, Tuǧrul. "Modeling with Kronecker Products." In Kronecker Modeling and Analysis of Multidimensional Markovian Systems, 13–46. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97129-2_2.

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2

Loan, C. F., and N. Pitsianis. "Approximation with Kronecker Products." In Linear Algebra for Large Scale and Real-Time Applications, 293–314. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-015-8196-7_17.

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3

Schroeder, Manfred R. "Fast Transformations and Kronecker Products." In Number Theory in Science and Communication, 196–200. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-662-22246-1_17.

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4

Schroeder, Manfred R. "Fast Transformation and Kronecker Products." In Number Theory in Science and Communication, 199–202. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-03430-9_17.

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5

Berck, Peter, and Knut Sydsæter. "Kronecker products and the vec operator." In Economists’ Mathematical Manual, 113–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-662-02678-6_22.

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Berck, Peter, and Knut Sydsæter. "Kronecker products and the vec operator." In Economists’ Mathematical Manual, 113–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-11597-8_22.

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7

Dayar, Tuğrul. "Introduction." In Analyzing Markov Chains using Kronecker Products, 1–7. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4190-8_1.

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Dayar, Tuğrul. "Preliminaries." In Analyzing Markov Chains using Kronecker Products, 9–19. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4190-8_2.

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Dayar, Tuğrul. "Iterative Methods." In Analyzing Markov Chains using Kronecker Products, 21–35. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4190-8_3.

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Dayar, Tuğrul. "Decompositional Methods." In Analyzing Markov Chains using Kronecker Products, 37–56. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4190-8_4.

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Тези доповідей конференцій з теми "Kronecker products"

1

Leskovec, Jure. "Networks, communities and kronecker products." In Proceeding of the 1st ACM international workshop. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1651274.1651275.

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2

Jokar, Sadegh. "Sparse recovery and Kronecker products." In 2010 44th Annual Conference on Information Sciences and Systems (CISS). IEEE, 2010. http://dx.doi.org/10.1109/ciss.2010.5464722.

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3

Nagy, James G., and Lisa Perrone. "Kronecker products in image restoration." In Optical Science and Technology, SPIE's 48th Annual Meeting, edited by Franklin T. Luk. SPIE, 2003. http://dx.doi.org/10.1117/12.512082.

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4

Liu, Xueting, and Hongkui Li. "On the Kippenhahn Curves of Kronecker Products." In 2009 IITA International Conference on Control, Automation and Systems Engineering, CASE 2009. IEEE, 2009. http://dx.doi.org/10.1109/case.2009.150.

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5

Li, Hongkui, Zhaowei Meng, Yunming Zhou, and Xueting Liu. "The Kippenhahn Curves of Some Kronecker Products." In 2009 ETP International Conference on Future Computer and Communication (FCC). IEEE, 2009. http://dx.doi.org/10.1109/fcc.2009.55.

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6

Alman, Josh. "Kronecker products, low-depth circuits, and matrix rigidity." In STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3406325.3451008.

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7

Dayar, Tugrul. "Analyzing Large Sparse Markov Chains of Kronecker Products." In 2009 Sixth International Conference on the Quantitative Evaluation of Systems (QEST). IEEE, 2009. http://dx.doi.org/10.1109/qest.2009.12.

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8

Zhao, Wenling, and Daojin Song. "About the kippenhahn curves of some kronecker products." In 2009 ISECS International Colloquium on Computing, Communication, Control, and Management (CCCM). IEEE, 2009. http://dx.doi.org/10.1109/cccm.2009.5267910.

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Liu, Jun, Su-qin Sun, and Xiao-hua Ou. "Notice of Retraction: Kronecker products of lattice-valued finite automata." In 2010 3rd IEEE International Conference on Computer Science and Information Technology (ICCSIT 2010). IEEE, 2010. http://dx.doi.org/10.1109/iccsit.2010.5565103.

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Mengran Xue and S. Roy. "Kronecker products of defective matrices: Some spectral properties and their implications on observability." In 2012 American Control Conference - ACC 2012. IEEE, 2012. http://dx.doi.org/10.1109/acc.2012.6315417.

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Звіти організацій з теми "Kronecker products"

1

Fulton, C. T., and L. Wu. Parallel computation of large least squares problems involving Kronecker products on the Connection Machine 5. Office of Scientific and Technical Information (OSTI), July 1995. http://dx.doi.org/10.2172/113992.

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2

Liang, Yuli, Chengcheng Hao, and Deliang Dai. Two-sample intraclass correlation coefficient tests for matrix-valued data. Department of Economics and Statistics, Linnaeus University, April 2024. http://dx.doi.org/10.15626/ns.wp.2024.06.

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Анотація:
Under a model having a Kronecker product covariance structure with compound symmetry or circular symmetry, two-sample hypothesis testing for the equality of two correlation parameters is considered. Different tests are proposed by using the ratio of independent F distributions. Several tests are compared with the proposed ones and practical recommendations are made based on their type I error probabilities and powers. Finally, all mentioned tests are applied to a real data example.
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