  In this paper, we consider the rank-one tensor completion problem. We address
the question of existence and uniqueness of the rank-one solution. In
particular we show that the global uniqueness over the field of real numbers
can be verified in a polynomial time. We give examples showing that there is an
essential difference between the question of global uniqueness over the fields
of real and complex numbers. Finally we briefly discuss the rank-one
approximation problem for noisy observations.
