Precision perturbation theory for quaternionic eigenvalues with gap-dependent bounds

Abstract In this paper, we present upper and lower bounds for eigenvalues of quaternionic Hermitian and non-Hermitian matrices under structured (especially rank-one) perturbations. Then we derive rigorous perturbation bounds for right eigenvalues of quaternionic matrices, extending classical results to the quaternions with particular attention to similarity classes of right eigenvalues. Numerical experiments demonstrate the superiority of our bounds in quaternionic continuation methods, with better improvements over existing approaches.