  Observations of the redshifted 21-cm line from the epoch of reionization have
recently motivated the construction of low frequency radio arrays with highly
redundant configurations. These configurations provide an alternative
calibration strategy - "redundant calibration" - and boosts sensitivity on
specific spatial scales. In this paper, we formulate calibration of redundant
interferometric arrays as a complex optimization problem. We solve this
optimization problem via the Levenberg-Marquardt algorithm. This calibration
approach is more robust to initial conditions than current algorithms and, by
leveraging an approximate matrix inversion, allows for further optimization and
an efficient implementation ("redundant StEfCal"). We also investigated using
the preconditioned conjugate gradient method as an alternative to the
approximate matrix inverse, but found that its computational performance is not
competitive with respect to "redundant StEfCal". The efficient implementation
of this new algorithm is made publicly available.
