  We consider the dynamical evolution of bound, hierarchical triples of
supermassive black holes that might be formed in the nuclei of galaxies
undergoing sequential mergers. The tidal force of the outer black hole on the
inner binary produces eccentricity oscillations through the Kozai mechanism,
and this can substantially reduce the gravitational wave merger time of the
inner binary. We numerically calculate the merger time for a wide range of
initial conditions and black hole mass ratios, including the effects of
octupole interactions in the triple as well as general relativistic periastron
precession in the inner binary. The semimajor axes and the mutual inclination
of the inner and outer binaries are the most important factors affecting the
merger time. We find that for a random distribution of inclination angles and
approximately equal mass black holes, it is possible to reduce the merger time
of a near circular inner binary by more than a factor of ten in over fifty
percent of all cases. We estimate that a typical exterior quadrupole moment
from surrounding matter in the galaxy may also be sufficient to excite
eccentricity oscillations in supermassive black hole binaries, and also
accelerate black hole mergers.
