Theory and Computation of Complex Tensors and Its Applications - Info and Reading Options

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Intro -- Preface -- References -- Contents -- 1 Introduction -- 1.1 Examples for Tensors -- 1.2 Basics of Tensors -- 1.2.1 Basic Operations -- 1.2.2 Structured Tensors -- 1.3 Basic Results -- 1.3.1 Tensor Spectral Theory -- 1.3.2 Real Tensor Rank-One Approximations -- 1.3.3 Complex Tensor Rank-One Approximations -- References -- 2 The Pseudo-Spectrum Theory -- 2.1 Preliminaries -- 2.2 Pseudo-Spectrum of a Complex Tensor -- 2.2.1 Definition and Properties -- 2.2.2 Computational Interpretation of ε-Pseudo-Spectrum -- 2.2.3 Pseudo-Spectral Abscissa and Radius -- 2.3 Pseudo-Spectrum for Tensor Polynomials -- 2.3.1 Definitions and Properties -- 2.3.2 Backward Errors -- 2.3.3 Nearest Irregular Tensor Polynomials -- 2.4 Further Discussions -- 2.4.1 An Example -- 2.4.2 Conclusion and Remarks -- References -- 3 Perturbation Theory -- 3.1 Preliminaries -- 3.1.1 Definitions -- 3.1.2 Symmetric and Mode-Symmetric Embeddings -- 3.2 Perturbation Bounds of Z- and H-Eigenvalues -- 3.2.1 Properties of Eigenvalues and Z-Eigenvalues -- 3.2.2 Algebraically Simple Z-Eigenvalues -- 3.2.3 Algebraically Simple Eigenvalues -- 3.2.4 Singular Values -- 3.3 Perturbation for the Tensor Polynomial Eigenvalue Problem -- 3.3.1 Tensor Generalized Eigenvalue Problem -- 3.3.2 Tensor Quadratic Eigenvalue Problem -- 3.3.3 Tensor Polynomial Eigenvalue Problem -- 3.4 The Smallest Eigenvalue of Nonsingular M-Tensors -- 3.4.1 An Inequality for the Perron Root -- 3.4.2 Perturbation of the Smallest Eigenvalue of M-Tensors -- 3.5 Numerical Examples -- 3.5.1 Verification of Inequalities -- 3.5.2 Verification of Perturbation Bounds -- References -- 4 Tensor Complementarity Problems -- 4.1 Preliminaries -- 4.1.1 Notation and Definitions -- 4.2 Lemmas and Problem Description -- 4.2.1 Lemmas -- 4.2.2 Problem Description -- 4.3 Main Results -- 4.3.1 Necessary Conditions

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