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Computing Inner Eigenvalues of Matrices in Tensor Train Matrix Format

In: Numerical Mathematics and Advanced Applications 2011

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  • T. Mach

    (Max Planck Institute for Dynamics of Complex Technical Systems)

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 $$\begin{array}{rcl} x_{i+1} = x_{i} - {B}^{-1}\left (Mx_{ i} - \mu (x_{i})x_{i}\right ),& & \\ \end{array}$$ and the folded spectrum method (replace M by $${(M - \sigma I)}^{2}$$ ). 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.

Suggested Citation

  • T. Mach, 2013. "Computing Inner Eigenvalues of Matrices in Tensor Train Matrix Format," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 781-788, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_82
    DOI: 10.1007/978-3-642-33134-3_82
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