  We consider the problem of decomposing a real-valued symmetric tensor as the
sum of outer products of real-valued, pairwise orthogonal vectors. Such
decompositions do not generally exist, but we show that some symmetric tensor
decomposition problems can be converted to orthogonal problems following the
whitening procedure proposed by Anandkumar et al. (2012). If an orthogonal
decomposition of an $m$-way $n$-dimensional symmetric tensor exists, we propose
a novel method to compute it that reduces to an $n \times n$ symmetric matrix
eigenproblem. We provide numerical results demonstrating the effectiveness of
the method.
