四元数矩阵特征值问题：保结构算法与应用（英文版）

　　Since the 1970s， Science Press has published more than thirty volumes in its series Monographs in Computational Methods. This series was established and led by the late academician， Feng Kang， the founding director of the Computing Center of the Chinese Academy of Sciences. The monograph series has provided timely information of the frontier directions and latest research results in computational mathematics. It has had great impact on young scientists and the entire research community， and has played a very important role in the development of computational mathematics in China.To cope with these new scientific developments， the Ministry of Education of the People's Republic of China in 1998 combined several subjects， such as computational mathematics， numerical algorithms， information science， and operations research and optimal control， into a new discipline called Information and Computational Science. As a result， Science Press also reorganized the editorial board of the monograph series and changed its name to Series in Information and Computational Science. The first editorial board meeting was held in Beijing in September 2004， and it discussed the new objectives， and the directions and contents of the new monograph series.The aim of the new series is to present the state of the art in Information and Computational Science to senior undergraduate and graduate students， as well as to scientists working in these fields. Hence， the series will provide concrete and systematic expositions of the advances in information and computational science， encompassing also related interdisciplinary developments.I would like to thank the previous editorial board members and assistants， and all the mathematicians who have contributed significantly to the monograph series on Computational Methods. As a result of their contributions the monograph series achieved an outstanding reputation in the community. I sincerely wish that we will extend this support to the new Series in Information and Computational Science， so that the new series can equally enhance the scientific development in information and computational science in this century.

暂缺《四元数矩阵特征值问题：保结构算法与应用（英文版）》作者简介

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 Decompositions
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 2x2 Block Structure Preserving Method
4．2．1 Structure-Preserving Method
4．2．2 Structure-Preserving Algorithm
4．2．3 Numerical Examples
4．3 4x4 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 Decomposition
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