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

页码：687 / 717

页数：31

共 45 条

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