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：特征值理论在对偶四元数埃尔米特矩阵中的应用对于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，提出采用瑞利商迭代计算该矩阵的极端特征值及其对应的特征向量。我们进一步推导了瑞利商迭代的收敛特性分析，证明其具有三次收敛率的局部收敛性。通过数值算例验证了所提出的瑞利商迭代法在处理对偶四元数埃尔米特特征值问题时的有效性。