Preprint No. MPIMD/11-09

Title: Computing Inner Eigenvalues of Matrices in Tensor Train Matrix Format

Author(s): Thomas Mach


Date: 2011-12-05


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 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


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{}},

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