Theory and Computation of Tensors: Multi-Dimensional Arrays

ISBN-13: 9780128039533 / Angielski / Miękka / 2016 / 148 str.

Yimin Wei; Weiyang Ding

Opis

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 algebra to numerical multi-linear algebra
• Offers examples of how researchers and students can engage in research and the applications of tensors and multi-dimensional arrays

Recenzje

"The book should be useful as a reference for research workers in linear algebra, operator theory, mathematical physics and numerical analysis." --MathSciNet

"Roughly half the book is devoted to defining and developing properties of tensors, and the other half to algorithms." --MAA Reviews

Spis treści

1. Introduction and Preliminaries

2. Hankel Tensors

3. Generalized Tensor Eigenvalue Problems

4. M-Tensors and Multi-Linear Equations5. Tensor Logarithmic Norms6. Multi-Linear Discriminant Analysis

O autorze

Yimin Wei is a Professor at the School of Mathematical Sciences, Fudan University, Shanghai, P.R. of China. He has has published three English books and over 100 research papers in international journals. His studies on tensors are supported by the National Natural Science Foundation of China. Weiyang Ding is a Ph.D student under the supervision of Professor Wei, at the School of Mathematical Sciences, Fudan University, Shanghai, P.R. of China.