Tensor Spaces and Numerical Tensor Calculus, Hackbusch Wolfgang
Автор: Hackbusch Название: Tensor Spaces and Numerical Tensor Calculus ISBN: 3642280269 ISBN-13(EAN): 9783642280269 Издательство: Springer Рейтинг: Цена: 15855.00 р. Наличие на складе: Нет в наличии.
Описание: Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n^d, where n^d 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. The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc. ?
Описание: This book takes the reader from the preliminary ideas of the Special Theory of Relativity (STR) to the doorsteps of the General Theory of Relativity (GTR).
Описание: Our self-contained volume provides an accessible introduction to linear and multilinear algebra as well as tensor calculus. Besides the standard techniques for linear algebra, multilinear algebra and tensor calculus, many advanced topics are included where emphasis is placed on the Kronecker product and tensor product. The Kronecker product has widespread applications in signal processing, discrete wavelets, statistical physics, Hopf algebra, Yang-Baxter relations, computer graphics, fractals, quantum mechanics, quantum computing, entanglement, teleportation and partial trace. All these fields are covered comprehensively.The volume contains many detailed worked-out examples. Each chapter includes useful exercises and supplementary problems. In the last chapter, software implementations are provided for different concepts. The volume is well suited for pure and applied mathematicians as well as theoretical physicists and engineers.New topics added to the third edition are: mutually unbiased bases, Cayley transform, spectral theorem, nonnormal matrices, Gateaux derivatives and matrices, trace and partial trace, spin coherent states, Clebsch-Gordan series, entanglement, hyperdeterminant, tensor eigenvalue problem, Carleman matrix and Bell matrix, tensor fields and Ricci tensors, and software implementations.
Описание: This advanced volume of lecture notes presents an open problem at the frontier of research into operator algebra theory, based on the author`s university lecture courses and written in a widely accessible style for researchers and Ph.D. students with little experience in the area.
Автор: Bhaben Chandra Kalita Название: Tensor Calculus and Applications: Simplified Tools and Techniques ISBN: 0367138069 ISBN-13(EAN): 9780367138066 Издательство: Taylor&Francis Рейтинг: Цена: 25265.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The aim of this book is to make the subject easier to understand. This book provides clear concepts, tools, and techniques to master the subject of Tensors, and can be used in many fields of research. Special applications are discussed in the book, in order to remove any confusion, and for absolute understanding of the subject.
Автор: Hackbusch Wolfgang Название: Tensor Spaces and Numerical Tensor Calculus ISBN: 3030355535 ISBN-13(EAN): 9783030355531 Издательство: Springer Рейтинг: Цена: 17074.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Special numerical techniques are already needed to deal with n x n matrices for large n. Tensor data are of size n x n x...x n=nd, where nd exceeds the computer memory by far. Since standard methods fail, a particular tensor calculus is needed to treat such problems.
Автор: Liqun Qi, Haibin Chen, Yannan Chen Название: Tensor Eigenvalues and their applications. ISBN: 9811080577 ISBN-13(EAN): 9789811080579 Издательство: Springer Рейтинг: Цена: 18294.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.
Название: Non-negative Matrix and Tensor Factorizations ISBN: 0470746661 ISBN-13(EAN): 9780470746660 Издательство: Wiley Рейтинг: Цена: 19000.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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).
Описание: Provides a systematic and example-rich guide to the basic properties and applications of tensor network methodologies, and demonstrates their promise as a tool for the analysis of extreme-scale multidimensional data. The book demonstrates the ability of tensor networks to provide linearly or even super-linearly, scalable solutions.
Автор: Pisier, Gilles (texas A & M University) Название: Tensor products of c*-algebras and operator spaces ISBN: 1108749119 ISBN-13(EAN): 9781108749114 Издательство: Cambridge Academ Рейтинг: Цена: 7762.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This advanced volume of lecture notes presents an open problem at the frontier of research into operator algebra theory, based on the author`s university lecture courses and written in a widely accessible style for researchers and Ph.D. students with little experience in the area.
This volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter.
The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field.
Автор: Khoromskij Boris N. Название: Tensor Numerical Methods in Scientific Computing ISBN: 3110370131 ISBN-13(EAN): 9783110370133 Издательство: Walter de Gruyter Цена: 45865.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
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
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