Theory And Computation Of Tensors

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Theory And Computation Of Tensors

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Author : Yimin Wei
language : en
Publisher: Academic Press
Release Date : 2016-08-28

Theory And Computation Of Tensors written by Yimin Wei and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-28 with Mathematics categories.

Theory and Computation of Tensors: Multi-Dimensional Arrays investigates theories and computations of tensors to broaden perspectives on matrices. Data in the Big Data Era is not only growing larger but also becoming much more complicated. Tensors (multi-dimensional arrays) arise naturally from many engineering or scientific disciplines because they can represent multi-relational data or nonlinear relationships. - Provides an introduction of recent results about tensors - Investigates theories and computations of tensors to broaden perspectives on matrices - Discusses how to extend numerical linear algebra to numerical multi-linear algebra - Offers examples of how researchers and students can engage in research and the applications of tensors and multi-dimensional arrays

Tensors For Data Processing

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Author : Yipeng Liu
language : en
Publisher: Academic Press
Release Date : 2021-10-21

Tensors For Data Processing written by Yipeng Liu and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-21 with Technology & Engineering categories.

Tensors for Data Processing: Theory, Methods and Applications presents both classical and state-of-the-art methods on tensor computation for data processing, covering computation theories, processing methods, computing and engineering applications, with an emphasis on techniques for data processing. This reference is ideal for students, researchers and industry developers who want to understand and use tensor-based data processing theories and methods. As a higher-order generalization of a matrix, tensor-based processing can avoid multi-linear data structure loss that occurs in classical matrix-based data processing methods. This move from matrix to tensors is beneficial for many diverse application areas, including signal processing, computer science, acoustics, neuroscience, communication, medical engineering, seismology, psychometric, chemometrics, biometric, quantum physics and quantum chemistry. - Provides a complete reference on classical and state-of-the-art tensor-based methods for data processing - Includes a wide range of applications from different disciplines - Gives guidance for their application

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.

Tensor Spaces And Numerical Tensor Calculus

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Author : Wolfgang Hackbusch
language : en
Publisher: Springer Nature
Release Date : 2019-12-16

Tensor Spaces And Numerical Tensor Calculus written by Wolfgang Hackbusch and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-16 with Mathematics categories.

Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.

Tensor Analysis

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Author : Liqun Qi
language : en
Publisher: SIAM
Release Date : 2017-04-19

Tensor Analysis written by Liqun Qi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-19 with Mathematics categories.

Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors.

Tensor Algebra And Tensor Analysis For Engineers

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Author : Mikhail Itskov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-04

Tensor Algebra And Tensor Analysis For Engineers written by Mikhail Itskov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-04 with Technology & Engineering categories.

There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.

Tensors

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Author : Anadi Jiban Das
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-05

Tensors written by Anadi Jiban Das and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-05 with Science categories.

Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.

An Introduction To Tensors And Group Theory For Physicists

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Author : Nadir Jeevanjee
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-26

An Introduction To Tensors And Group Theory For Physicists written by Nadir Jeevanjee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-26 with Science categories.

An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Advanced undergraduate and graduate students in physics and applied mathematics will find clarity and insight into the subject in this textbook.

Atomic And Molecular Nonlinear Optics Theory Experiment And Computation

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Author : G. Maroulis
language : en
Publisher: IOS Press
Release Date : 2011-05-27

Atomic And Molecular Nonlinear Optics Theory Experiment And Computation written by G. Maroulis and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-27 with Science categories.

The papers collected in this volume in honor of the late Stanisław Kielich cover an impressive range of modern subjects in molecular science. These subjects include, among others, the nonlinear optics of molecules, new approaches to the electronic structure of large molecules, the properties of carbon nanotubes, fluorescence polarization spectroscopy, computational studies of systems of fundamental interest to collision-induced spectroscopy, the simulation of fluids, NLO materials, chemical bonding in complex molecules, the NLO properties of functionalized DNA and the magnetic properties of molecular assemblies. Written by eminent specialists, the papers should offer valuable guidance to a wide community of graduate students and researchers.

Tensors For Physics

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Author : Siegfried Hess
language : en
Publisher: Springer
Release Date : 2015-04-25

Tensors For Physics written by Siegfried Hess and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-25 with Science categories.

This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-trace formulas, coupling of irreducible tensors, rotation of tensors. Constitutive laws for optical, elastic and viscous properties of anisotropic media are dealt with. The anisotropic media include crystals, liquid crystals and isotropic fluids, rendered anisotropic by external orienting fields. The dynamics of tensors deals with phenomena of current research. In the last section, the 3D Maxwell equations are reformulated in their 4D version, in accord with special relativity.