  Transit timing variations - deviations from strict periodicity between
successive passages of a transiting planet - can be used to probe the structure
and dynamics of multiple-planet systems. In this paper, we examine prospects
for numerically solving the so-called inverse problem, the determination of the
orbital elements of a perturbing body from the transit timing variations it
induces. We assume that the planetary systems under examination have a limited
number of Doppler velocity measurements, and show that a more extensive radial
velocity characterization with precision comparable to the semiamplitude of the
perturber may remove degeneracies in the solution. We examine several
configurations of interest, including (1) a prototypical non-resonant system,
modeled after HD40307 b and c, which contains multiple super-Earth mass
planets, (2) a hypothetical system containing a transiting giant planet with a
terrestrial-mass companion trapped in low-order mean motion resonance, and (3)
the HAT-P-13 system, in which forced precession by an outer perturbing body
that is well characterized by Doppler radial velocity measurements can give
insight into the interior structure of a perturbing planet, and for which the
determination of mutual inclination between the transiting planet and its
perturber is a key issue.
