  Present day computers do not have enough memory to store the high-dimensional
tensors required when using
  a direct product basis to compute vibrational energy levels of a polyatomic
molecule with more than about 5 atoms.
  One way to deal with this problem is to represent tensors using a tensor
format. In this paper, we use CP format. Energy levels are computed by building
a basis from vectors obtained by solving linear equations. The method can be
thought of as a CP realization of a block inverse iteration method with
multiple shifts. The CP rank of the tensors is fixed and the linear equations
are solved with an Alternating Least Squares method. There is no need for rank
reduction, no need for orthogonalization, and tensors with rank larger than the
fixed rank used to solve the linear equations are never generated. The ideas
are tested by computing vibrational energy levels of a 64-D bilinearly coupled
model Hamiltonian and of acetonitrile(12-D).
