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.
1. Chapter 1: Introduction and Preliminaries - p. 3 2. Chapter 2: Generalized Tensor Eigenvalue Problems - p. 11 3. Abstract - p. 11 4. 2.1 A Unified Framework - p. 11 5. 2.2 Basic Definitions - p. 13 6. 2.3 Several Basic Properties - p. 14 7. 2.4 Real Tensor Pairs - p. 20 8. 2.5 Sign-Complex Spectral Radius - p. 26 9. 2.6 An Illustrative Example - p. 34 10. II: Hankel Tensors - p. 36 11. Chapter 3: Fast Tensor-Vector Products - p. 39 12. Chapter 4: Inheritance Properties - p. 59 13. III: M-Tensors - p. 77 14. Chapter 5: Definitions and Basic Properties - p. 81 15. Chapter 6: Multilinear Systems with M-Tensors - p. 97 16. Abstract - p. 97 17. 6.1 Motivations - p. 97 18. 6.2 Triangular Equations - p. 99 19. 6.3 M-Equations and Beyond - p. 102 20. 6.4 Iterative Methods for M-Equations - p. 108 21. 6.5 Perturbation Analysis of M-Equations - p. 114 22. 6.6 Inverse Iteration - p. 118 23. Appendix - p. 122 24. Bibliography - p. 125 25. Subject Index - p. 135
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.
1. Chapter 1: Introduction and Preliminaries - p. 3 2. Chapter 2: Generalized Tensor Eigenvalue Problems - p. 11 3. Abstract - p. 11 4. 2.1 A Unified Framework - p. 11 5. 2.2 Basic Definitions - p. 13 6. 2.3 Several Basic Properties - p. 14 7. 2.4 Real Tensor Pairs - p. 20 8. 2.5 Sign-Complex Spectral Radius - p. 26 9. 2.6 An Illustrative Example - p. 34 10. II: Hankel Tensors - p. 36 11. Chapter 3: Fast Tensor-Vector Products - p. 39 12. Chapter 4: Inheritance Properties - p. 59 13. III: M-Tensors - p. 77 14. Chapter 5: Definitions and Basic Properties - p. 81 15. Chapter 6: Multilinear Systems with M-Tensors - p. 97 16. Abstract - p. 97 17. 6.1 Motivations - p. 97 18. 6.2 Triangular Equations - p. 99 19. 6.3 M-Equations and Beyond - p. 102 20. 6.4 Iterative Methods for M-Equations - p. 108 21. 6.5 Perturbation Analysis of M-Equations - p. 114 22. 6.6 Inverse Iteration - p. 118 23. Appendix - p. 122 24. Bibliography - p. 125 25. Subject Index - p. 135
