Computing Inner Eigenvalues of Matrices in Tensor Train Matrix Format

T. Mach ()
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T. Mach: Max Planck Institute for Dynamics of Complex Technical Systems

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 781-788 from Springer

Abstract: 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.

Keywords: Tensor Train; Oseledets; Local Rank; Inexact Newton Method; Compressed Storage Scheme (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_82

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DOI: 10.1007/978-3-642-33134-3_82

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