1. Randomized block Krylov subspace algorithms for low-rank quaternion matrix approximations.
- Author
-
Li, Chaoqian, Liu, Yonghe, Wu, Fengsheng, and Che, Maolin
- Subjects
LOW-rank matrices ,KRYLOV subspace ,APPROXIMATION error ,SINGULAR value decomposition ,QUATERNIONS ,QUATERNION functions - Abstract
A randomized quaternion singular value decomposition algorithm based on block Krylov iteration (RQSVD-BKI) is presented to solve the low-rank quaternion matrix approximation problem. The upper bounds of deterministic approximation error and expected approximation error for the RQSVD-BKI algorithm are also given. It is shown by numerical experiments that the running time of the RQSVD-BKI algorithm is smaller than that of the quaternion singular value decomposition, and the relative errors of the RQSVD-BKI algorithm are smaller than those of the randomized quaternion singular value decomposition algorithm in Liu et al. (SIAM J. Sci. Comput., 44(2): A870-A900 (2022)) in some cases. In order to further illustrate the feasibility and effectiveness of the RQSVD-BKI algorithm, we use it to deal with the problem of color image inpainting. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF