Computing transfer function dominant poles of large-scale second-order dynamical systems. A new algorithm for the computation of dominant poles of transfer functions of large-scale second-order dynamical systems is presented: the quadratic dominant pole algorithm (QDPA). The algorithm works directly with the system matrices of the original system, so no linearization is needed. To improve global convergence, the QDPA uses subspace acceleration, and deflation of found dominant poles is implemented in a very efficient way. The dominant poles and corresponding eigenvectors can be used to construct structure-preserving modal approximations and also to improve reduced-order models computed by Krylov subspace methods, as is illustrated by numerical results.