# Theory 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 tensorsInvestigates theories and computations of tensors to broaden perspectives on matricesDiscusses how to extend numerical linear algebra to numerical multi-linear algebraOffers examples of how researchers and students can engage in research and the applications of tensors and multi-dimensional arrays

Produk Detail:

• Author : Yimin Wei
• Pages : 148 pages
• ISBN : 9780128039533
• Rating : 4/5 from 21 reviews

## Theory and Computation of Tensors • Author : Yimin Wei,Weiyang Ding
• Release : 01 September 2016

"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 tensorsInvestigates theories and computations of tensors to broaden perspectives on matricesDiscusses how to extend numerical linear algebra to

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

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

## Theory and Computation of Tensors • Author : Yimin Wei,Weiyang Ding
• Release : 28 August 2016

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 • Author : Maolin Che,Yimin Wei
• Publisher : Springer
• Release : 29 April 2020

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 • Author : Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki
• Publisher : Springer
• Release : 18 March 2016

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

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

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

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

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

## Vectors, Tensors and the Basic Equations of Fluid Mechanics • Author : Rutherford Aris
• Publisher : Courier Corporation
• Release : 28 August 2012

Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.

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

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 • Author : Pavel Grinfeld
• Publisher : Springer Science & Business Media
• Release : 24 September 2013

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,

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

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,

## An Introduction to Semi-tensor Product of Matrices and Its Applications • Author : Daizhan Cheng,Hongsheng Qi,Yin Zhao
• Publisher : World Scientific
• Release : 25 October 2021

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.

## 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

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

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

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 on Tensor Analysis and their Applications • Author : Francisco Bulnes
• Publisher : BoD – Books on Demand
• Release : 09 September 2020

This book brings together recent advances in tensor analysis and studies of its invariants such as twistors, spinors, kinematic tensors and others belonging to tensor algebras with extended structures to Lie algebras, Kac-Moody algebras, and enveloping algebras, among others. Chapters cover such topics as classical tensors and bilinear forms, tensors for exploring space–time, tensor applications in geometry and continuum media, and advanced topics in tensor analysis such as invariant theory, derived categories, hypercohomologies, k-modules, extensions of kinematic tensors, infinite