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Theory and Computation of Complex Tensors and its Applications

  • Book
  • © 2020

Overview

Authors:
  1. Maolin Che

    1. School of Economics Mathematics, Southwestern University of Finance and Economics, Chengdu, China

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  2. Yimin Wei

    1. School of Mathematical Sciences, Fudan University, Shanghai, China

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  • Introduces the neural network models and Takagi factorization for the computation of tensor rank-one approximations and US- (U-) eigenvalues

  • Enriches the properties of nonnegative tensors, defines the sign nonsingular tensors and derives a probabilistic algorithm for locating a positive diagonal in a nonnegative tensors

  • Gives adaptive randomized algorithms for the computation of the low multilinear rank approximations and the tensor train approximations of the tensors

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Maolin Che, Yimin Wei
    Pages 1-17

  3. The Pseudo-Spectrum Theory

    • Maolin Che, Yimin Wei
    Pages 19-49

  4. Perturbation Theory

    • Maolin Che, Yimin Wei
    Pages 51-96

  5. Tensor Complementarity Problems

    • Maolin Che, Yimin Wei
    Pages 97-115

  6. Plane Stochastic Tensors

    • Maolin Che, Yimin Wei
    Pages 117-146

  7. Neural Networks

    • Maolin Che, Yimin Wei
    Pages 147-186

  8. US- and U-Eigenpairs of Complex Tensors

    • Maolin Che, Yimin Wei
    Pages 187-214

  9. Randomized Algorithms

    • Maolin Che, Yimin Wei
    Pages 215-246

  10. Back Matter

    Pages 247-250
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Keywords

About this book

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.

Authors and Affiliations

  • School of Economics Mathematics, Southwestern University of Finance and Economics, Chengdu, China

    Maolin Che

  • School of Mathematical Sciences, Fudan University, Shanghai, China

    Yimin Wei

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