Theory and Computation of Complex Tensors and its Applications

1. Front Matter

   Pages i-xii

   PDF

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

    PDF

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.

• tensor spectral theory
• tensor complementarity problems
• nonnegative tensors
• U-eigenpairs
• randomized algorithms
• US-eigenvalues
• randomized algorithms
• matrix theory

• 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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