  Fitting a Candecomp/Parafac (CP) decomposition (also known as Canonical
Polyadic decomposition) to a multi-way array or higher-order tensor, is
equivalent to finding a best low-rank approximation to the multi-way array or
higher-order tensor, where the rank is defined as the outer-product rank.
However, such a best low-rank approximation may not exist due to the fact that
the set of multi-way arrays with rank at most $R$ is not closed for $R\ge 2$.
Nonexistence of a best low-rank approximation results in (groups of) diverging
rank-1 components when an attempt is made to compute the approximation. In this
note, we show that in a group of two or three diverging components, the
components converge to proportionality almost everywhere. A partial proof of
this result for larger groups of diverging components is also given. Also, we
give examples of groups of three, four, and six non-proportional diverging
components. These examples are shown to be exceptional cases.
