信息与计算科学丛书四元数矩阵特征值问题——保结构算法与应用(英文版)

内容简介

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本书主要研究四元数矩阵特征值问题的理论与算法以及在彩色图像识别中的应用。首先，我们介绍两类四元数矩阵特征值问题，即左特征值问题和右特征值问题。在理论上，分析两类问题的可解性、解的专享性、扰动性等。其次，给出求解四元数矩阵右特征值的保结构算法，包括直接方法和迭代算法。然后，分析迭代算法的收敛性。很后给出四元数特征值问题的应用，包括彩色图像填充、人脸识别、主成分分析等

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目录

Contents Chapter 1 Introduction 1 Chapter 2 Basic Quaternion Matrix Theory 7 2.1 Quaternion Matrices 7 2.2 Quaternion Matrix Eigenvalue Problems 8 2.3 Unitary Quaternion Transformations 10 2.3.1 Improved Householder-Based Transformations 10 2.3.2 Generalized Quaternion Givens Transformations 12 2.4 Complex and Real Counterpart Methods 13 2.5 JRS-Symmetric Matrices 18 Chapter 3 General Quaternion Matrix Eigenvalue Problem 22 3.1 Structure-Preserving QR Algorithm 22 3.1.1 The Upper JRS-Hessenberg Form 23 3.1.2 Structure-Preserving Decompositions 25 3.1.3 The Structure-Preserving JRS-Hessenberg QR Iteration 27 3.2 Quaternion QR Algorithm 35 3.2.1 The Quaternion Hessenberg Reduction 36 3.2.2 Quaternion Hessenberg QR Factorization 39 3.2.3 Implicit Double Shift Quaternion QR Algorithm 40 3.2.4 Numerical Examples 44 3.3 The Power and Inverse Power Methods 48 3.3.1 The Power Method 48 3.3.2 The Inverse Power Method 58 3.4 Perturbation Theory 60 3.4.1 The Perturbation of Eigenvalues 61 3.4.2 Simple Eigenpairs 65 3.5 Conclusion 68 Chapter 4 Hermitian Quaternion Matrix Eigenvalue Problem 69 4.1 Background 69 4.2 2×2 Block Structure Preserving Method 71 4.2.1 Structure-Preserving Method 71 4.2.2 Structure-Preserving Algorithm 804.2.3 Numerical Examples 82 4.3 4×4 Block Structure-Preserving Method 86 4.3.1 Structure-Preserving Tridiagonalizing 87 4.3.2 Right Eigenvalue Problem 92 4.3.3 Structure-Preserving Algorithm 92 4.3.4 Numerical Examples 96 4.4 Structure-Preserving Jacobi Algorithm 100 4.4.1 History of Jacobi Algorithm 100 4.4.2 Structure-Preserving Jacobi Algorithm 101 4.4.3 Numerical Examples 111 4.5 Lanczos Method for Large-Scale Quaternion Singular Value Decomposition 114 4.5.1 History of Lancozos Method 115 4.5.2 The Quaternion Lanczos Method 115 4.5.3 Lanczos-Based Algorithms 118 4.5.4 Numerical Examples 122 4.6 Conclusion 125 Chapter 5 Applications 127 5.1 Quaternion Principal Component Analysis 127 5.1.1 Representation and Compression of Color Face Images 129 5.1.2 Face Recognition in Color 129 5.1.3 Experiments 131 5.2 Two Dimensional Quaternion Principal Component Analysis 135 5.2.1 Color 2DPCA Approach 135 5.2.2 Experiments 138 5.3 Color Image Inpainting 141 5.3.1 Preliminaries 141 5.3.2 Robust Quaternion Matrix Completion 142 5.3.3 Experiments 144 5.4 Color Watermarking 149 5.4.1 Embedding and Extracting Procedure 149 5.4.2 Evaluation Criteria 152 5.4.3 Experiments 152 5.5 Conclusion 154 Bibliography 156 Book list of the Series in Information and Computational Science 162 Color Figures

封面

书名:信息与计算科学丛书四元数矩阵特征值问题——保结构算法与应用(英文版)

作者:贾志刚

页数:176

定价:¥88.0

出版社:科学出版社

出版日期:2020-05-01

ISBN:9787030638878

PDF电子书大小:123MB 高清扫描完整版