Computational Mathematics and Mathematical Physics

, Volume 55, Issue 10, pp 1606–1618 | Cite as

Weighted versions of Gl-FOM and Gl-GMRES for solving general coupled linear matrix equations

  • Fatemeh Panjeh Ali Beik
  • Davod Khojasteh Salkuyeh


In this paper, two algorithms called weighted Gl-FOM (WGl-FOM) and weighted Gl-GMRES (WGl-GMRES) are proposed for solving the general coupled linear matrix equations. In order to accelerate the speed of convergence, a new inner product is used. Invoking the new inner product and a new matrix product, the weighted global Arnoldi algorithm is introduced which will be utilized for employing the WGl-FOM and WGl-GMRES algorithms to solve the linear coupled linear matrix equations. After introducing the weighted methods, some relations that link Gl-FOM (Gl-GMRES) to its weighted version are established. Numerical experiments are presented to illustrate the effectiveness of the new algorithms in comparison with Gl-FOM and Gl-GMRES algorithms for solving the linear coupled linear matrix equations.


linear matrix equation Krylov subspace weighted methods global FOM global GMRES global Arnoldi 


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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  • Fatemeh Panjeh Ali Beik
    • 1
  • Davod Khojasteh Salkuyeh
    • 2
  1. 1.Department of MathematicsVali-e-Asr University of RafsanjanRafsanjanIran
  2. 2.Faculty of Mathematical SciencesUniversity of GuilanRashtIran

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