The application of eigenvalue theory to dual quaternion Hermitian matrix holds significance in the realm of multi-agent formation control. In this paper, we focus on the numerical algorithm for the right eigenvalue of a dual quaternion Hermitian matrix. Rayleigh quotient iteration is proposed for computing the extreme eigenvalue with the associated eigenvector of the dual quaternion Hermitian matrix. We also derive an analysis of the convergence characteristics of the Rayleigh quotient iteration, which exhibits a local convergence rate of cubic. Numerical examples are provided to illustrate the efficiency of the proposed Rayleigh quotient iteration for the dual quaternion Hermitian eigenvalue problem.

翻译：将特征值理论应用于对偶四元数埃尔米特矩阵，在多智能体编队控制领域具有重要意义。本文聚焦于对偶四元数埃尔米特矩阵右特征值的数值算法，针对该矩阵的极值特征值及其对应特征向量的计算，提出瑞利商迭代法。我们进一步推导了瑞利商迭代法的收敛特性分析，表明其具有三次局部收敛速率。数值算例验证了所提瑞利商迭代法求解对偶四元数埃尔米特特征值问题的有效性。