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math.NA2025
On Eigenvector Computation and Eigenvalue Reordering for the Non-Hermitian Quaternion Eigenvalue Problem
Zhigang Jia, Meiyue Shao, Yanjun Shao
In this paper we present several additions to the quaternion QR algorithm, including algorithms for eigenvector computation and eigenvalue reordering. A key outcome of the eigenval…
math.NA2025
A Novel Adaptive Low-Rank Matrix Approximation Method for Image Compression and Reconstruction
Weiwei Xu, Weijie Shen, Chang Liu +1
Low-rank matrix approximation plays an important role in various applications such as image processing, signal processing and data analysis. The existing methods require a guess of…
math.NA2024
Flexible Quaternion Generalized Minimal Residual Method for Ill-Posed Quaternion Inverse Problems
Xuan Liu, Zhigang Jia, Xiaoqing Jin
The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dim…