Numerical Algorithms

, Volume 13, Issue 1, pp 45–60 | Cite as

Preconditioned Barzilai-Borwein method for the numerical solution of partial differential equations

  • Brigida Molina
  • Marcos Raydan


The preconditioned Barzilai-Borwein method is derived and applied to the numerical solution of large, sparse, symmetric and positive definite linear systems that arise in the discretization of partial differential equations. A set of well-known preconditioning techniques are combined with this new method to take advantage of the special features of the Barzilai-Borwein method. Numerical results on some elliptic test problems are presented. These results indicate that the preconditioned Barzilai-Borwein method is competitive and sometimes preferable to the preconditioned conjugate gradient method.


Barzilai-Borwein method conjugate gradient method incomplete Cholesky symmetric successive overrelaxation elliptic equations 

AMS subject classification

65F10 65F15 65L10 65N20 


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Copyright information

© J.C. Baltzer AG, Science Publishers 1996

Authors and Affiliations

  • Brigida Molina
    • 1
  • Marcos Raydan
    • 1
  1. 1.Dpto. de Computación, Facultad de CienciasUniversidad Central de VenezuelaCaracasVenezuela

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