Название: Theory and Computation of Complex Tensors and its Applications
Автор: Maolin Che, Yimin Wei
Издательство: Springer
Год: 2020
Страниц: 258
Язык: английский
Формат: pdf (true), epub
Размер: 27.7 MB

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.

An increasing number of applications in signal processing, data analysis and higher-order statistics, as well as independent component analysis involve the manipulation of data whose elements are addressed by more than two indices. In the literature, these higher-order extensions of vectors (first-order) and matrices (second-order) are called higher-order tensors , multi-dimensional matrices , or multiway arrays. Tensor problems have wide applications in chemometrics, signal processing and high order statistics.

Generally speaking, there are two kinds of tensors: a data structure, which admits different dimensions according to the complexity of the data; or an operator, where it possesses different meanings in different situations. All tensors mentioned in this book can be viewed as a data structure.

In this book, the computations are carried out in MATLAB Version 2013a and the MATLAB Tensor Toolbox on a laptop with an Intel Core i5-4200M CPU (2.50 GHz) and a 8.00 GB RAM.

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.