The behaviour of the magnetic field produced by spherical kinematic dynamos at large magnetic Reynolds number for two stationary axisymmetric roll flows is examined. Five numerical techniques to solve the large banded eigenvalue problems, which arise for the growth rate of the magnetic field, are compared, particularly their performance when eigenvalues are closely clustered. The five eigenvalue methods are inverse iteration, orthogonal iteration, lop-sided iteration, the implicitly restarted Arnoldi method and the non-symmetric Lanczos method. A shift and invert strategy was employed to obtain the growth rates of largest real part
