The implicitly restarted multi-symplectic block-Lanczos method for large-scale Hermitian quaternion matrix eigenvalue problem and applications

The large-scale Hermitian quaternion eigenvalue problem has become the key issue of color image recognition. However, there are still lack of efficient iterative methods of computing its partial eigenpairs. To solve this problem, a new implicitly restarted multi-symplectic block-Lanczos method is proposed with generalizing the block and implicit restarting techniques to quaternion matrix eigenvalue computation. The proposed algorithm is applied to color image identification and approximation, and the experimental results demonstrate its efficiency and advantages to the existing algorithms.