A structure-preserving Jacobi algorithm for quaternion Hermitian eigenvalue problems

A new real structure-preserving Jacobi algorithm is proposed for solving the eigenvalue problem of quaternion Hermitian matrix. By employing the generalized JRS-symplectic Jacobi rotations, the new quaternion Jacobi algorithm can preserve the symmetry and JRS-symmetry of the real counterpart of quat...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2018-02, Vol.75 (3), p.809-820
Main Authors: Ma, Ru-Ru, Jia, Zhi-Gang, Bai, Zheng-Jian
Format: Article
Language:English
Subjects:
Algorithms
Conservation laws
Eigenvalues
Jacobi rotation
Mathematical analysis
Matrix methods
Quaternion Hermitian eigenvalue problem
Quaternions
Real counterpart
Rotation
Structure-preserving algorithm
Symmetry
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Summary:A new real structure-preserving Jacobi algorithm is proposed for solving the eigenvalue problem of quaternion Hermitian matrix. By employing the generalized JRS-symplectic Jacobi rotations, the new quaternion Jacobi algorithm can preserve the symmetry and JRS-symmetry of the real counterpart of quaternion Hermitian matrix. Moreover, the proposed algorithm only includes real operations without dimension-expanding and is generally superior to the state-of-the-art algorithm. Numerical experiments are reported to indicate its efficiency and accuracy.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2017.10.009