Journal of Scientific Computing

, Volume 77, Issue 2, pp 950–970 | Cite as

Limited Memory Block Preconditioners for Fast Solution of Fractional Partial Differential Equations

  • Daniele BertacciniEmail author
  • Fabio Durastante


An innovative block structured with sparse blocks multi iterative preconditioner for linear multistep formulas used in boundary value form is proposed here to accelerate GMRES, FGMRES and BiCGstab(l). The preconditioner is based on block \(\omega \)-circulant matrices and a short-memory approximation of the underlying Jacobian matrix of the fractional partial differential equations. Convergence results, numerical tests and comparisons with other techniques confirm the effectiveness of the approach.


Preconditioners Fractional calculus Krylov iterative methods 

Mathematics Subject Classification

65F08 65M22 35R11 



We wish to thank two anonymous referees for their constructive comments which have improved the readability of the paper.


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Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomeItaly
  2. 2.Istituto per le Applicazioni del Calcolo (IAC) “M. Picone”National Research Council (CNR)RomeItaly
  3. 3.Dipartimento di InformaticaUniversità di PisaPisaItaly

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