In this paper, we generalize the Jacobi eigenvalue algorithm to compute all eigenvalues and eigenvectors of a dual quaternion Hermitian matrix and show the convergence. We also propose a three-step Jacobi eigenvalue algorithm to compute the eigenvalues when a dual quaternion Hermitian matrix has two eigenvalues with identical standard parts but different dual parts and prove the convergence. Numerical experiments are presented to illustrate the efficiency and stability of the proposed Jacobi eigenvalue algorithm compaired to the power method and the Rayleigh quotient iteration method.

翻译：本文推广了雅可比特征值算法，用于计算对偶四元数埃尔米特矩阵的全部特征值和特征向量，并证明了其收敛性。针对标准部分相同但对偶部分相异的双特征值情形，我们进一步提出了一种三步雅可比特征值算法来计算特征值，并证明了该算法的收敛性。数值实验表明，与幂法和瑞利商迭代法相比，所提出的雅可比特征值算法在计算效率和数值稳定性方面均表现出优越性。