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 deitions
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 deition
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 ponent analysis
5.1.1 representation and pression of color face images
5.1.2 face recognition in color
5.1.3 experiments
5.2 two dimensional quaternion principal ponent 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 pletion
5.3.3 experiments
5.4 color watermarking
5.4.1 embed and extracting procedure
5.4.2 evaluation criteria
5.4.3 experiments
5.5 conclusion
bibliography
book list of the series in information and putational science
color figures
内容简介:
thi book i intended to provide the fundamental material for young reearcher of the quaternion matrix eigenvalue problem.tarting from the origin of the right eigenvalue problem of quaternion matricewe introduce the baic theory and method of quaternion matrice in the firt chapter.in the econd chapterwe tudy the eigenvalue problem of general quaternion matriceinclu the tructurepreerving qr algorithmthe quaternion qr algorithmetc.in the third chapterwe reearch the eigenvahie problem of hermitian quaternion matricewith proing two kind of direct method uing the houeholder tranform and two iterative method: jacobi algorithm and lanczo method.in the lat chapterwe provide everal practical application modeluch a two dimenional principle ponent analyi and color image inpaintingwhich relying on olving the quaternion eigenvalue problem.the writing of thi book i traight forward and i addreed to reader who have a baic graduate mathematic background.alternativelyit may be ued in a beginning graduate level coure and a a reference.
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