Theory and Computation of Tensors

Theory and Computation of Tensors
  • Author : Yimin Wei,Weiyang Ding
  • Publisher : Academic Press
  • Release : 28 August 2016
GET THIS BOOKTheory and Computation of Tensors

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

Theory and Computation of Complex Tensors and its Applications

Theory and Computation of Complex Tensors and its Applications
  • Author : Maolin Che,Yimin Wei
  • Publisher : Springer Nature
  • Release : 01 April 2020
GET THIS BOOKTheory and Computation of Complex Tensors and its Applications

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

Algebraic and Computational Aspects of Real Tensor Ranks

Algebraic and Computational Aspects of Real Tensor Ranks
  • Author : Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki
  • Publisher : Springer
  • Release : 18 March 2016
GET THIS BOOKAlgebraic and Computational Aspects of Real Tensor Ranks

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

An Introduction to Semi-tensor Product of Matrices and Its Applications

An Introduction to Semi-tensor Product of Matrices and Its Applications
  • Author : Daizhan Cheng,Hongsheng Qi,Yin Zhao
  • Publisher : World Scientific
  • Release : 02 August 2021
GET THIS BOOKAn Introduction to Semi-tensor Product of Matrices and Its Applications

Proposes a generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP). This book offers a comprehensive introduction to the theory of STP and its various applications, including logical function, fuzzy control, Boolean networks, analysis and control of nonlinear systems, amongst others.

Tensors

Tensors
  • Author : J. M. Landsberg
  • Publisher : American Mathematical Soc.
  • Release : 14 December 2011
GET THIS BOOKTensors

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

Tensor Analysis

Tensor Analysis
  • Author : Liqun Qi,Ziyan Luo
  • Publisher : SIAM
  • Release : 19 April 2017
GET THIS BOOKTensor Analysis

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

Introduction to Tensor Analysis and the Calculus of Moving Surfaces

Introduction to Tensor Analysis and the Calculus of Moving Surfaces
  • Author : Pavel Grinfeld
  • Publisher : Springer Science & Business Media
  • Release : 24 September 2013
GET THIS BOOKIntroduction to Tensor Analysis and the Calculus of Moving Surfaces

This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds,

Physical Components of Tensors

Physical Components of Tensors
  • Author : Wolf Altman,Antonio Marmo De Oliveira
  • Publisher : CRC Press
  • Release : 08 October 2018
GET THIS BOOKPhysical Components of Tensors

Illustrating the important aspects of tensor calculus, and highlighting its most practical features, Physical Components of Tensors presents an authoritative and complete explanation of tensor calculus that is based on transformations of bases of vector spaces rather than on transformations of coordinates. Written with graduate students, professors, and researchers in the areas of elasticity and shell theories in mind, this text focuses on the physical and nonholonomic components of tensors and applies them to the theories. It establishes a theory

Atomic and Molecular Nonlinear Optics: Theory, Experiment and Computation

Atomic and Molecular Nonlinear Optics: Theory, Experiment and Computation
  • Author : G. Maroulis,T. Bancewicz,B. Champagne
  • Publisher : IOS Press
  • Release : 27 May 2011
GET THIS BOOKAtomic and Molecular Nonlinear Optics: Theory, Experiment and Computation

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

Computational Multiscale Modeling of Fluids and Solids

Computational Multiscale Modeling of Fluids and Solids
  • Author : Martin Oliver Steinhauser
  • Publisher : Springer
  • Release : 29 November 2016
GET THIS BOOKComputational Multiscale Modeling of Fluids and Solids

The idea of the book is to provide a comprehensive overview of computational physics methods and techniques, that are used for materials modeling on different length and time scales. Each chapter first provides an overview of the basic physical principles which are the basis for the numerical and mathematical modeling on the respective length-scale. The book includes the micro-scale, the meso-scale and the macro-scale, and the chapters follow this classification. The book explains in detail many tricks of the trade

Advances in Theory and Practice of Computational Mechanics

Advances in Theory and Practice of Computational Mechanics
  • Author : Lakhmi C. Jain,Margarita N. Favorskaya,Ilia S. Nikitin,Dmitry L. Reviznikov
  • Publisher : Springer Nature
  • Release : 31 March 2020
GET THIS BOOKAdvances in Theory and Practice of Computational Mechanics

This book discusses physical and mathematical models, numerical methods, computational algorithms and software complexes, which allow high-precision mathematical modeling in fluid, gas, and plasma mechanics; general mechanics; deformable solid mechanics; and strength, destruction and safety of structures. These proceedings focus on smart technologies and software systems that provide effective solutions to real-world problems in applied mechanics at various multi-scale levels. Highlighting the training of specialists for the aviation and space industry, it is a valuable resource for experts in the

Tensor Spaces and Numerical Tensor Calculus

Tensor Spaces and Numerical Tensor Calculus
  • Author : Wolfgang Hackbusch
  • Publisher : Springer Nature
  • Release : 16 December 2019
GET THIS BOOKTensor Spaces and Numerical Tensor Calculus

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,

Conformal Field Theories and Tensor Categories

Conformal Field Theories and Tensor Categories
  • Author : Chengming Bai,Jürgen Fuchs,Yi-Zhi Huang,Liang Kong,Ingo Runkel,Christoph Schweigert
  • Publisher : Springer Science & Business Media
  • Release : 30 October 2013
GET THIS BOOKConformal Field Theories and Tensor Categories

The present volume is a collection of seven papers that are either based on the talks presented at the workshop "Conformal field theories and tensor categories" held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories

Tensors

Tensors
  • Author : Anadi Jiban Das
  • Publisher : Springer Science & Business Media
  • Release : 05 October 2007
GET THIS BOOKTensors

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.