Convergence of the Dominant Pole Algorithm and Rayleigh Quotient Iteration

The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. In this paper, two methods for the computation of the dominant poles of a large scale transfer function are studied: two-sided Rayleigh Quotient Iteration (RQI) and the Dominant Pole Algorithm (DPA). Firstly, a local convergence analysis of DPA will be given, and the local convergence neighborhoods of the dominant poles will be characterized for both methods. Secondly, theoretical and numerical results will be presented that indicate that for DPA the basins of attraction of the dominant pole are larger than for two-sided RQI. The price for the better global convergence is only a few additional iterations, due to the asymptotically quadratic rate of convergence of DPA, against the cubic rate of two-sided RQI.