A metric function for dual quaternion matrices and related least-squares problems

Chen Ling; Chenjian Pan; Liqun Qi

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arXiv · 2411.05306

A metric function for dual quaternion matrices and related least-squares problems

Chen Ling·Chenjian Pan·Liqun Qi

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Abstract

Solving dual quaternion equations is an important issue in many fields such as scientific computing and engineering applications. In this paper, we first introduce a new metric function for dual quaternion matrices. Then, we reformulate dual quaternion overdetermined equations as a least squares problem, which is further converted into a bi-level optimization problem. Numerically, we propose two implementable proximal point algorithms for finding approximate solutions of dual quaternion overdetermined equations. The relevant convergence theorems %and computational complexity estimates have also been established. Preliminary simulation results on synthetic and color image datasets demonstrate the effectiveness of the proposed algorithms.

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Chen Ling, Chenjian Pan, Liqun Qi. 2024-11-08. A metric function for dual quaternion matrices and related least-squares problems. https://arxiv.org/abs/2411.05306

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