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Book
Advances on Tensor Analysis and their Applications
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ISBN: 1839625562 1839625554 Year: 2020 Publisher: London : IntechOpen,

Tensor analysis
Authors: ---
ISBN: 1281876852 9786611876852 9812564462 9789812564467 9789812383600 9812383603 9781281876850 9812383603 6611876855 Year: 2003 Publisher: Singapore World Scientific

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Abstract

Tensor analysis is an essential tool in any science (e.g. engineering,physics, mathematical biology) that employs a continuum description. This concise text offers a straight forward treatment of the subject suitable for the student or practicing engineer.


Book
Irreducible Cartesian Tensors
Author:
ISBN: 3110563738 3110564866 9783110564860 9783110564877 3110564874 3110563630 9783110563733 9783110563634 3110563630 Year: 2017 Publisher: Berlin Boston

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This monograph covers the concept of cartesian tensors with the needs and interests of physicists, chemists and other physical scientists in mind. After introducing elementary tensor operations and rotations, spherical tensors, combinations of tensors are introduced, also covering Clebsch-Gordan coefficients. After this, readers from the physical sciences will find generalizations of the results to spinors and applications to quantum mechanics.


Book
Tensor Numerical Methods in Scientific Computing
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ISBN: 3110391392 311036591X 9783110365917 Year: 2018 Publisher: Berlin Boston

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The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximation of multivariate functions and operators by using the appropriate tensor formats. The old and new rank-structured tensor formats are investigated. We discuss in detail the novel quantized tensor approximation method (QTT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FFT and wavelet transforms. This book suggests the constructive recipes and computational schemes for a number of real life problems described by the multidimensional partial differential equations. We present the theory and algorithms for the sinc-based separable approximation of the analytic radial basis functions including Green's and Helmholtz kernels. The efficient tensor-based techniques for computational problems in electronic structure calculations and for the grid-based evaluation of long-range interaction potentials in multi-particle systems are considered. We also discuss the QTT numerical approach in many-particle dynamics, tensor techniques for stochastic/parametric PDEs as well as for the solution and homogenization of the elliptic equations with highly-oscillating coefficients. Contents Theory on separable approximation of multivariate functions Multilinear algebra and nonlinear tensor approximation Superfast computations via quantized tensor approximation Tensor approach to multidimensional integrodifferential equations


Book
Tensor computation for data analysis
Author:
ISBN: 3030743861 3030743853 Year: 2022 Publisher: Cham, Switzerland : Springer,


Book
Dynamic network representation based on latent factorization of tensors
Authors: --- ---
ISBN: 9811989346 9811989338 Year: 2023 Publisher: Singapore : Springer,

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Abstract

A dynamic network is frequently encountered in various real industrial applications, such as the Internet of Things. It is composed of numerous nodes and large-scale dynamic real-time interactions among them, where each node indicates a specified entity, each directed link indicates a real-time interaction, and the strength of an interaction can be quantified as the weight of a link. As the involved nodes increase drastically, it becomes impossible to observe their full interactions at each time slot, making a resultant dynamic network High Dimensional and Incomplete (HDI). An HDI dynamic network with directed and weighted links, despite its HDI nature, contains rich knowledge regarding involved nodes’ various behavior patterns. Therefore, it is essential to study how to build efficient and effective representation learning models for acquiring useful knowledge. In this book, we first model a dynamic network into an HDI tensor and present the basic latent factorization of tensors (LFT) model. Then, we propose four representative LFT-based network representation methods. The first method integrates the short-time bias, long-time bias and preprocessing bias to precisely represent the volatility of network data. The second method utilizes a proportion-al-integral-derivative controller to construct an adjusted instance error to achieve a higher convergence rate. The third method considers the non-negativity of fluctuating network data by constraining latent features to be non-negative and incorporating the extended linear bias. The fourth method adopts an alternating direction method of multipliers framework to build a learning model for implementing representation to dynamic networks with high preciseness and efficiency.


Book
Tensor calculus
Author:
ISBN: 0444411240 9780444411242 Year: 1974 Publisher: Amsterdam


Book
Tensor geometry : the geometric viewpoint and its uses
Authors: ---
ISBN: 0273003178 9780273003175 Year: 1977 Publisher: London Pitman

A brief on tensor analysis
Author:
ISBN: 0387906398 1468401432 1468401416 9780387906393 Year: 1982 Publisher: New York (N.Y.): Springer


Book
Theory and computation of tensors : multi-dimensional arrays
Authors: ---
ISBN: 0128039809 0128039531 9780128039809 9780128039533 Year: 2016 Publisher: Waltham, MA : Elsevier,

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