  We propose a new algorithm for tensor decomposition, based on Jennrich's
algorithm, and apply our new algorithmic ideas to blind deconvolution and
Gaussian mixture models. Our first contribution is a simple and efficient
algorithm to decompose certain symmetric overcomplete order-3 tensors, that is,
three dimensional arrays of the form $T = \sum_{i=1}^n a_i \otimes a_i \otimes
a_i$ where the $a_i$s are not linearly independent.Our algorithm comes with a
detailed robustness analysis. Our second contribution builds on top of our
tensor decomposition algorithm to expand the family of Gaussian mixture models
whose parameters can be estimated efficiently. These ideas are also presented
in a more general framework of blind deconvolution that makes them applicable
to mixture models of identical but very general distributions, including all
centrally symmetric distributions with finite 6th moment.
