Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (1): 94-109.doi: 10.1007/s42967-024-00408-8

• ORIGINAL PAPERS • Previous Articles     Next Articles

Developing LSQR Method for Sylvester Quaternion Tensor Equations

Qiu-Yi Chen, Yi-Gui Ou, Xin-Fang Zhang   

  1. School of Mathematics and Statistics, Hainan University, Haikou, 570228, Hainan, China
  • Received:2023-12-20 Revised:2024-03-28 Online:2026-02-20 Published:2026-02-11
  • Contact: Xin-Fang Zhang,E-mail:995272@hainanu.edu.cn E-mail:995272@hainanu.edu.cn
  • Supported by:
    This research was supported by the National Natural Science Foundation of China (Grant No. 11961018), and the Hainan Provincial Natural Science Foundation of China (Grant No. 122MS001).

Abstract: In this paper, we consider solving a least-squares problem to the generalized Sylvester quaternion tensor equation. From the properties of quaternions and the Kronecker product, a tensor form of the LSQR algorithm is proposed for solving this problem, the convergence analysis of which is then established. Numerical results are reported to illustrate the feasibility and validity of the proposed algorithm compared with the tensor form of the CGLS method, including when the algorithm is tested with some randomly generated data and color video restoration problems.

Key words: Sylvester quaternion tensor equation, Tensor form, LSQR, Color video restoration

CLC Number: