  Space missions like CoRoT and Kepler have provided numerous new observations
of stellar oscillations in a multitude of stars by high precision photometry.
This work compares the observed rich oscillation spectrum of the rapidly
rotating B3 IV star HD 43317 with the first results obtained by a new method to
calculate unstable oscillation modes in rapidly rotating stars in order to see
whether some of the observed modes can be identified. The new numerical method
consists of two parts. We first search for modes resonant with a prescribed
forcing symmetry by moving through relevant regions of complex frequency space
and monitoring any increase of the stellar response to the applied forcing and
zooming in onto the resonance. These resonant non-adiabatic 2D-solutions are
then fed into a 2D relaxation code with the same equations but without forcing
terms. The complex oscillation frequency used in the forcing is now no longer
prescribed, but added as an extra unknown. The corresponding free oscillation
mode is usually obtained after a few ($<10$) iterations with only minor
adjustment of the complex oscillation frequency. To compare with the observed
light variations we calculate the `visibility' of the found unstable
oscillation modes, taking into account the cancellation of the various parts of
the radiating oscillating stellar surface as seen by the observer. The
frequencies of unstable axisymmetric g-modes, which have the highest
visibility, appear to nearly coincide with the observed largest amplitude
photometric variations of HD 43317, making an identification of the latter
oscillations as $m$=0 modes plausible. The identification of $m$=1 g-modes is
less straightforward, while many of the unstable even $m$=2 g-modes may
correspond to observed weaker photometric variations.
