Abstract: The computation of eigenvalues is one of the core topics of numerical mathematics. We will discuss an eigenvalue algorithm for the computation of inner eigenvalues of a large, symmetric, and positive definite matrix M based on the preconditioned inverse iteration xi+1 = xi - B-1 (Mxi - (xi) xi), and the folded spectrum method (replace M by (M-I)). We assume that M is given in the tensor train matrix format and use the TT-toolbox from I.V. Oseledets (see http://spring.inm.ras.ru/osel/) for the numerical computations. We will present first numerical results and discuss the numerical difficulties. A shorted version of this preprint was submitted to the Proceedings of the ENUMATH 2011 (Leicester).