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Hermitian矩阵中的应用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Hermitian矩阵右特征值的数值算法。针对对偶四元数Hermitian矩阵，提出采用Rayleigh商迭代计算其极端特征值及对应特征向量。本文还对Rayleigh商迭代的收敛特性进行了分析，证明其具有三次局部收敛速度。通过数值算例验证了所提出的Rayleigh商迭代在对偶四元数Hermitian特征值问题中的有效性。