# Preprint No. MPIMD/11-09

#### Author(s): Thomas Mach

#### Email: thomas.mach@googlemail.com

#### Date: 2011-12-05

#### 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

x_{i+1} = x_{i} - B^{-1}
(Mx_{i} - μ(x_{i}) x_{i}),

and the folded spectrum method (replace M by (M-σI)²). 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).

There is additional material
(source code) available for this preprint under http://www.mpi-magdeburg.mpg.de/preprints/2011/1109/

#### BibTeX:

@TECHREPORT{MPIMD11-09,

author = {Thomas Mach},

title = {Computing Inner Eigenvalues
of Matrices in Tensor Train Matrix
Format},

number = {MPIMD/11-09},

month = dec,

year = 2011,

institution = {Max Planck Institute Magdeburg},

type = {Preprint},

note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},

}