四元数矩阵特征值问题——保结构算法与应用（英文版）

定　　价：88 元

丛书名：信息与计算科学丛书

• 作者：贾志刚
• 出版时间：2020/5/21
• ISBN：9787030638878
• 出 版 社：科学出版社

• 中图法分类：O151.21 
• 页码：176
• 纸张：胶版纸
• 版次：1
• 开本：32开

内容简介

This book is intended to provide the fundamental material for young researchers of the quaternion matrix eigenvalue problem. Starting from the origin of the right eigenvalue problem of quaternion matrices, we introduce the basic theory and methods of quaternion matrices in the first chapter. In the second chapter, we study the eigenvalue problem of general quaternion matrices, including the st等

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目 录

Contents
Chapter 1 Introduction
Chapter 2 Basic Quaternion Matrix Theory
2.1 Quaternion Matrices
2.2 Quaternion Matrix Eigenvalue Problems
2.3 Unitary Quaternion Transformations
2.3.1 Improved Householder-Based Transformations
2.3.2 Generalized Quaternion Givens Transformations
2.4 Complex and Real Counterpart Methods
2.5 JRS-Symmetric Matrices
Chapter 3 General Quaternion Matrix Eigenvalue Problem
3.1 Structure-Preserving QR Algorithm
3.1.1 The Upper JRS-Hessenberg Form
3.1.2 Structure-Preserving Decomitions
3.1.3 The Structure-Preserving JRS-Hessenberg QR Iteration
3.2 Quaternion QR Algorithm
3.2.1 The Quaternion Hessenberg Reduction
3.2.2 Quaternion Hessenberg QR Factorization
3.2.3 Implicit Double Shift Quaternion QR 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 Quaternion 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
4.2.3 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 Quaternion Singular Value Decomition
4.5.1 History of Lancozos Method
4.5.2 The Quaternion Lanczos Method
4.5.3 Lanczos-Based Algorithms
4.5.4 Numerical Examples
4.6 Conclusion
Chapter 5 Applications
5.1 Quaternion 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 Quaternion 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 Quaternion Matrix Completion
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