Algebraic And Computational Aspects Of Real Tensor Ranks
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Algebraic And Computational Aspects Of Real Tensor Ranks
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Author : Toshio Sakata
language : en
Publisher: Springer
Release Date : 2016-03-18
Algebraic And Computational Aspects Of Real Tensor Ranks written by Toshio Sakata and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-18 with Mathematics categories.
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through simultaneous singular value decompositions.
Theory And Computation Of Complex Tensors And Its Applications
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Author : Maolin Che
language : en
Publisher: Springer Nature
Release Date : 2020-04-01
Theory And Computation Of Complex Tensors And Its Applications written by Maolin Che and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-01 with Mathematics categories.
The book provides an introduction of very recent results about the tensors and mainly focuses on the authors' work and perspective. A systematic description about how to extend the numerical linear algebra to the numerical multi-linear algebra is also delivered in this book. The authors design the neural network model for the computation of the rank-one approximation of real tensors, a normalization algorithm to convert some nonnegative tensors to plane stochastic tensors and a probabilistic algorithm for locating a positive diagonal in a nonnegative tensors, adaptive randomized algorithms for computing the approximate tensor decompositions, and the QR type method for computing U-eigenpairs of complex tensors. This book could be used for the Graduate course, such as Introduction to Tensor. Researchers may also find it helpful as a reference in tensor research.
A Survey Of Lie Groups And Lie Algebras With Applications And Computational Methods
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Author : Johan G. F. Belinfante
language : en
Publisher: SIAM
Release Date : 1989-01-01
A Survey Of Lie Groups And Lie Algebras With Applications And Computational Methods written by Johan G. F. Belinfante and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.
Introduces the concepts and methods of the Lie theory in a form accessible to the non-specialist by keeping mathematical prerequisites to a minimum. Although the authors have concentrated on presenting results while omitting most of the proofs, they have compensated for these omissions by including many references to the original literature. Their treatment is directed toward the reader seeking a broad view of the subject rather than elaborate information about technical details. Illustrations of various points of the Lie theory itself are found throughout the book in material on applications. In this reprint edition, the authors have resisted the temptation of including additional topics. Except for correcting a few minor misprints, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed.
Computational Algebra
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Author : Klaus G. Fischer
language : en
Publisher: CRC Press
Release Date : 1993-10-18
Computational Algebra written by Klaus G. Fischer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-18 with Mathematics categories.
Based on the fifth Mid-Atlantic Algebra Conference held recently at George Mason University, Fairfax, Virginia. Focuses on both the practical and theoretical aspects of computational algebra. Demonstrates specific computer packages, including the use of CREP to study the representation of theory for finite dimensional algebras and Axiom to study algebras of finite rank.
Decomposability Of Tensors
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Author : Luca Chiantini
language : en
Publisher: MDPI
Release Date : 2019-02-15
Decomposability Of Tensors written by Luca Chiantini and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-15 with Mathematics categories.
This book is a printed edition of the Special Issue "Decomposability of Tensors" that was published in Mathematics
Introduction To Vector And Tensor Analysis
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Author : Robert C. Wrede
language : en
Publisher: Courier Corporation
Release Date : 1972-06-01
Introduction To Vector And Tensor Analysis written by Robert C. Wrede and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-06-01 with Mathematics categories.
Text for advanced undergraduate and graduate students covers the algebra, differentiation, and integration of vectors, and the algebra and analysis of tensors, with emphasis on transformation theory
Concepts From Tensor Analysis And Differential Geometry By Tracy Y Thomas
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Author :
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Concepts From Tensor Analysis And Differential Geometry By Tracy Y Thomas written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Mathematics categories.
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Tensors Geometry And Applications
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Author : J. M. Landsberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-12-14
Tensors Geometry And Applications written by J. M. Landsberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-14 with Mathematics categories.
Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.
High Performance Tensor Computations In Scientific Computing And Data Science
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Author : Edoardo Angelo Di Napoli
language : en
Publisher: Frontiers Media SA
Release Date : 2022-11-08
High Performance Tensor Computations In Scientific Computing And Data Science written by Edoardo Angelo Di Napoli and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-08 with Science categories.
Tensor Calculus For Engineers
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Author : Reint de Boer
language : en
Publisher:
Release Date : 2006-09-01
Tensor Calculus For Engineers written by Reint de Boer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-01 with Calculus of tensors categories.
This textbook introduces to the vector and tensor calculus as it is used in continuum mechanics. Therefore, it limits itself to the 3-dimensional Euclidian space. It contains, in addition, an introduction to continuum mechanics and linear shell theory. The theoretical concepts of small and finite strain elasticity, its numerical formulation and essential implementation aspects are presented in detail. After setting the variational framework of boundary value problems, several Finite Element representations are discussed. The formulation of isotropic and anisotropic elasticity is performed within a basis-independent formalism. As far as possible illustrative approaches are chosen although some of the concepts require axiomatic introduction. All chapters widely consist of examples and exercises. This book is written mainly for students in civil and mechanical engineering and bridges the gap between mathematics and its engineering application.