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醉染图书四元数矩阵特征值问题:保结构算法与应用9787030638878
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Chapter 1 Introduction
Chapter 2 Basic ternion Matrix Theory
2.1 ternion Matrices
2.2 ternion Matrix Eigenvalue Problems
. Unitary ternion Transformations
..1 Improved Householder-Based Transformations
..2 Generalized ternion Givens Transformations
2.4 Complex and Real Counterpart Methods
2.5 JRS-Symmetric Matrices
Chapter 3 General ternion Matrix Eigenvalue Problem
3.1 Structure-Preserving R Algorithm
3.1.1 The Upper JRS-Hessenberg Form
3.1.2 Structure-Preserving Decoitions
3.1.3 The Structure-Preserving JRS-Hessenberg R Iteration
3.2 ternion R Algorithm
3.2.1 The ternion Hessenberg Reduction
3.2.2 ternion Hessenberg R Factorization
3.. Implicit Double Shift ternion R Algorithm
3.2.4 Numerical Examples
3.3 The Power and Inverse Power Methods
3.3.1 The Power Method
3.3.2 The Inverse Power Method
3.4 Perturbation Theory
3.4.1 The Perturbation of Eigenvalues
3.4.2 Simple Eigenpairs
3.5 Conclusion
Chapter 4 Hermitian ternion Matrix Eigenvalue Problem
4.1 Background
4.2 2×2 Block Structure Preserving Method
4.2.1 Structure-Preserving Method
4.2.2 Structure-Preserving Algorithm
4.. Numerical Examples
4.3 4×4 Block Structure-Preserving Method
4.3.1 Structure-Preserving Tridiagonalizing
4.3.2 Right Eigenvalue Problem
4.3.3 Structure-Preserving Algorithm
4.3.4 Numerical Examples
4.4 Structure-Preserving Jacobi Algorithm
4.4.1 History of Jacobi Algorithm
4.4.2 Structure-Preserving Jacobi Algorithm
4.4.3 Numerical Examples
4.5 Lanczos Method for Large-Scale ternion Singular Value Decoition
4.5.1 History of Lancozos Method
4.5.2 The ternion Lanczos Method
4.5.3 Lanczos-Based Algorithms
4.5.4 Numerical Examples
4.6 Conclusion
Chapter 5 Applications
5.1 ternion Principal Component Analysis
5.1.1 Representation and Compression of Color Face Images
5.1.2 Face Recognition in Color
5.1.3 Experiments
5.2 Two Dimensional ternion Principal Component Analysis
5.2.1 Color 2DPCA Approach
5.2.2 Experiments
5.3 Color Image Inpainting
5.3.1 Preliminaries
5.3.2 Robust ternion Matrix Comlio
5.3.3 Experiments
5.4 Color Watermarking
5.4.1 Embedding and Extracting Procedure
5.4.2 Evaluation Criteria
5.4.3 Experiments
5.5 Conclusion
Bibliography
Book list of the Series in Information and Computational Science
Color Figures
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