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 - μ(xi) xi),
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/