Circulant preconditioners for a kind of spatial fractional diffusion equations

Zhi Wei Fang, Kwok Po NG, Hai Wei Sun*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

15 Citations (Scopus)


In this paper, circulant preconditioners are studied for discretized matrices arising from finite difference schemes for a kind of spatial fractional diffusion equations. The fractional differential operator is comprised of left-sided and right-sided derivatives with order in (12,1). The resulting discretized matrices preserve Toeplitz-like structure and hence their matrix-vector multiplications can be computed efficiently by the fast Fourier transform. Theoretically, the spectra of the circulant preconditioned matrices are shown to be clustered around 1 under some conditions. Numerical experiments are presented to demonstrate that the preconditioning technique is very efficient.

Original languageEnglish
Pages (from-to)729-747
Number of pages19
JournalNumerical Algorithms
Issue number2
Publication statusPublished - 1 Oct 2019

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • Circulant preconditioner
  • Fast Fourier transform
  • Fractional diffusion equation
  • Krylov subspace methods
  • Toeplitz matrix


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