Theory And Computation Of Complex Tensors And Its Applications
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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.
Applied Linear Algebra Probability And Statistics
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Author : Ravindra B. Bapat
language : en
Publisher: Springer Nature
Release Date : 2023-07-31
Applied Linear Algebra Probability And Statistics written by Ravindra B. Bapat and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.
This book focuses on research in linear algebra, statistics, matrices, graphs and their applications. Many chapters in the book feature new findings due to applications of matrix and graph methods. The book also discusses rediscoveries of the subject by using new methods. Dedicated to Prof. Calyampudi Radhakrishna Rao (C.R. Rao) who has completed 100 years of legendary life and continues to inspire us all and Prof. Arbind K. Lal who has sadly departed us too early, it has contributions from collaborators, students, colleagues and admirers of Professors Rao and Lal. With many chapters on generalized inverses, matrix analysis, matrices and graphs, applied probability and statistics, and the history of ancient mathematics, this book offers a diverse array of mathematical results, techniques and applications. The book promises to be especially rewarding for readers with an interest in the focus areas of applied linear algebra, probability and statistics.
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.
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 Computation For Seismic Data Processing
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Author : Feng Qian
language : en
Publisher: Springer Nature
Release Date : 2025-04-26
Tensor Computation For Seismic Data Processing written by Feng Qian and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-26 with Science categories.
This book aims to provide a comprehensive understanding of tensor computation and its applications in seismic data analysis, exclusively catering to seasoned researchers, graduate students, and industrial engineers alike. Tensor emerges as a natural representation of multi-dimensional modern seismic data, and tensor computation can help prevent possible harm to the multi-dimensional geological structure of the subsurface that occurred in classical seismic data analysis. It delivers a wealth of theoretical, computational, technical, and experimental details, presenting an engineer's perspective on tensor computation and an extensive investigation of tensor-based seismic data analysis techniques. Embark on a transformative exploration of seismic data processing—unlock the potential of tensor computation and reshape your approach to high-dimensional geological structures. The discussion begins with foundational chapters, providing a solid background in both seismic data processing and tensor computation. The heart of the book lies in its seven chapters on tensor-based seismic data analysis methods. From structured low-tubal-rank tensor completion to cutting-edge techniques like tensor deep learning and tensor convolutional neural networks, each method is meticulously detailed. The superiority of tensor-based data analysis methods over traditional matrix-based data analysis approaches is substantiated through synthetic and real field examples, showcasing their prowess in handling high-dimensional modern seismic data. Notable chapters delve into seismic noise suppression, seismic data interpolation, and seismic data super-resolution using advanced tensor models. The final chapter provides a cohesive summary of the conclusion and future research directions, ensuring readers facilitate a thorough understanding of tensor computation applications in seismic data processing. The appendix includes a hatful of information on existing tensor computation software, enhancing the book's practical utility.
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.
Progress And Visions In Quantum Theory In View Of Gravity
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Author : Felix Finster
language : en
Publisher: Springer Nature
Release Date : 2020-04-09
Progress And Visions In Quantum Theory In View Of Gravity written by Felix Finster and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-09 with Science categories.
This book focuses on a critical discussion of the status and prospects of current approaches in quantum mechanics and quantum field theory, in particular concerning gravity. It contains a carefully selected cross-section of lectures and discussions at the seventh conference “Progress and Visions in Quantum Theory in View of Gravity” which took place in fall 2018 at the Max Planck Institute for Mathematics in the Sciences in Leipzig. In contrast to usual proceeding volumes, instead of reporting on the most recent technical results, contributors were asked to discuss visions and new ideas in foundational physics, in particular concerning foundations of quantum field theory. A special focus has been put on the question of which physical principles of quantum (field) theory can be considered fundamental in view of gravity. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.
Tensor Network Contractions
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Author : Shi-Ju Ran
language : en
Publisher: Springer Nature
Release Date : 2020-01-27
Tensor Network Contractions written by Shi-Ju Ran and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-27 with Science categories.
Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.
Computational Contact Mechanics
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Author : Alexander Konyukhov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-14
Computational Contact Mechanics written by Alexander Konyukhov 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 2012-08-14 with Science categories.
This book contains a systematical analysis of geometrical situations leading to contact pairs -- point-to-surface, surface-to-surface, point-to-curve, curve-to-curve and curve-to-surface. Each contact pair is inherited with a special coordinate system based on its geometrical properties such as a Gaussian surface coordinate system or a Serret-Frenet curve coordinate system. The formulation in a covariant form allows in a straightforward fashion to consider various constitutive relations for a certain pair such as anisotropy for both frictional and structural parts. Then standard methods well known in computational contact mechanics such as penalty, Lagrange multiplier methods, combination of both and others are formulated in these coordinate systems. Such formulations require then the powerful apparatus of differential geometry of surfaces and curves as well as of convex analysis. The final goals of such transformations are then ready-for-implementation numerical algorithms within the finite element method including any arbitrary discretization techniques such as high order and isogeometric finite elements, which are most convenient for the considered geometrical situation. The book proposes a consistent study of geometry and kinematics, variational formulations, constitutive relations for surfaces and discretization techniques for all considered geometrical pairs and contains the associated numerical analysis as well as some new analytical results in contact mechanics.
Nonnegative Matrix And Tensor Factorizations
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Author : Andrzej Cichocki
language : en
Publisher: John Wiley & Sons
Release Date : 2009-07-10
Nonnegative Matrix And Tensor Factorizations written by Andrzej Cichocki and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-10 with Science categories.
This book provides a broad survey of models and efficient algorithms for Nonnegative Matrix Factorization (NMF). This includes NMF’s various extensions and modifications, especially Nonnegative Tensor Factorizations (NTF) and Nonnegative Tucker Decompositions (NTD). NMF/NTF and their extensions are increasingly used as tools in signal and image processing, and data analysis, having garnered interest due to their capability to provide new insights and relevant information about the complex latent relationships in experimental data sets. It is suggested that NMF can provide meaningful components with physical interpretations; for example, in bioinformatics, NMF and its extensions have been successfully applied to gene expression, sequence analysis, the functional characterization of genes, clustering and text mining. As such, the authors focus on the algorithms that are most useful in practice, looking at the fastest, most robust, and suitable for large-scale models. Key features: Acts as a single source reference guide to NMF, collating information that is widely dispersed in current literature, including the authors’ own recently developed techniques in the subject area. Uses generalized cost functions such as Bregman, Alpha and Beta divergences, to present practical implementations of several types of robust algorithms, in particular Multiplicative, Alternating Least Squares, Projected Gradient and Quasi Newton algorithms. Provides a comparative analysis of the different methods in order to identify approximation error and complexity. Includes pseudo codes and optimized MATLAB source codes for almost all algorithms presented in the book. The increasing interest in nonnegative matrix and tensor factorizations, as well as decompositions and sparse representation of data, will ensure that this book is essential reading for engineers, scientists, researchers, industry practitioners and graduate students across signal and image processing; neuroscience; data mining and data analysis; computer science; bioinformatics; speech processing; biomedical engineering; and multimedia.