On the cubic convergence of the Paardekooper method

We show a simple way how asymptotic convergence results can be conveyed from a simple Jacobi method to a block Jacobi method. Our pilot methods are the well known symmetric Jacobi method and the Paardekooper method for reducing a skew-symmetric matrix to the real Schur form. We show resemblance in the quadratic and cubic convergence estimates, but also discrepances in the asymptotic assumptions. By numerical tests we confirm that our asymptotic assumptions for the Paardekooper method are most general.