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Numerical Algorithms

, Volume 70, Issue 2, pp 407–426 | Cite as

A key to choose subspace size in implicitly restarted Arnoldi method

  • S. A. Shahzadeh Fazeli
  • Nahid EmadEmail author
  • Zifan Liu
Original Paper

Abstract

The implicitly restarted Arnoldi method (IRAM) computes some eigenpairs of large sparse non Hermitian matrices. However, the size of the subspace in this method is chosen empirically. A poor choice of this size could lead to the non-convergence of the method. In this paper we propose a technique to improve the choice of the size of subspace. This approach, called multiple implicitly restarted Arnoldi method with nested subspaces (MIRAMns) is based on the projection of the problem on several nested subspaces instead of a single one. Thus, it takes advantage of several different sized subspaces. MIRAMns updates the restarting vector of an IRAM by taking the eigen-information of interest obtained in all subspaces into account. With almost the same complexity as IRAM, according to our experiments, MIRAMns improves the convergence of IRAM.

Keywords

Large eigenproblems Krylov subspace size Arnoldi method Implicit restarting 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • S. A. Shahzadeh Fazeli
    • 1
  • Nahid Emad
    • 2
    Email author
  • Zifan Liu
    • 2
  1. 1.Faculty of MathematicsYazd UniversityYazdIran
  2. 2.Maison de la simulation and PRiSM LaboratoryUniversity of VersaillesVersaillesFrance

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