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Computational Methods in Applied Mathematics

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Volume 19, Issue 1

Issues

A Low-Rank Inexact Newton–Krylov Method for Stochastic Eigenvalue Problems

Peter Benner
  • Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
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/ Akwum Onwunta
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  • Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
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/ Martin Stoll
  • Faculty of Mathematics, Professorship Scientific Computing, Technische Universität Chemnitz, 09107 Chemnitz, Germany
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Published Online: 2018-07-21 | DOI: https://doi.org/10.1515/cmam-2018-0030

Abstract

This paper aims at the efficient numerical solution of stochastic eigenvalue problems. Such problems often lead to prohibitively high-dimensional systems with tensor product structure when discretized with the stochastic Galerkin method. Here, we exploit this inherent tensor product structure to develop a globalized low-rank inexact Newton method with which we tackle the stochastic eigenproblem. We illustrate the effectiveness of our solver with numerical experiments.

Keywords: Stochastic Galerkin System; Krylov Methods; Eigenvalues; Eigenvectors; Low-Rank Solution; Preconditioning

MSC 2010: 35R60; 60H15; 60H35; 65N22; 65F10; 65F50

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About the article

Received: 2017-12-09

Revised: 2018-01-19

Accepted: 2018-05-02

Published Online: 2018-07-21

Published in Print: 2019-01-01


The work was performed while Martin Stoll was at the Max Planck Institute for Dynamics of Complex Technical Systems.


Citation Information: Computational Methods in Applied Mathematics, Volume 19, Issue 1, Pages 5–22, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2018-0030.

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