A new structure-preserving method for quaternion Hermitian eigenvalue problems

In this paper we propose a novel structure-preserving algorithm for solving the right eigenvalue problem of quaternion Hermitian matrices. The algorithm is based on the structure-preserving tridiagonalization of the real counterpart for quaternion Hermitian matrices by applying orthogonal JRSJRS-symplectic matrices. The algorithm is numerically stable because we use orthogonal transformations; the algorithm is very efficient, it costs about a quarter arithmetical operations, and a quarter to one-eighth CPU times, comparing with standard general-purpose algorithms. Numerical experiments are provided to demonstrate the efficiency of the structure-preserving algorithm.