Randomized block Krylov subspace algorithms for low-rank quaternion matrix approximations

被引：4
|
作者：
Li, Chaoqian [1 ]
Liu, Yonghe [1 ]
Wu, Fengsheng [1 ]
Che, Maolin [2 ]
机构：
[1] Yunnan Univ, Sch Math & Stat, Kunming 650091, Peoples R China
[2] Southwestern Univ Finance & Econ, Sch Math, Chengdu 611130, Peoples R China
来源：
NUMERICAL ALGORITHMS | 2024年 / 96卷 / 02期
关键词：
Low-rank quaternion matrix approximation; Quaternion singular value decomposition; Randomized quaternion singular value decomposition; Block Krylov iteration; SINGULAR-VALUE DECOMPOSITION; COLOR IMAGES; COMPLETION;
D O I：
10.1007/s11075-023-01662-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：687 / 717
页数：31
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