Fourier analysis of frequency filtering decomposition preconditioners

Qiang Niu*, Lin Zhang Lu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, frequency filtering decomposition (FFD) preconditioner is analyzed by the approach of Fourier analysis. The condition number estimation of a preconditioned 2-D model problem is presented. Analysis reveals that condition number of the preconditioned matrix grows like O (h- 1), with h be the mesh size. By using the framework of FFD, a stabilized frequency filtering decomposition (SFFD) method is proposed and analyzed by Fourier method. Results show that SFFD preconditioner is superior to FFD preconditioner in the sense that κ (MSFFD- 1 A) ≤ κ (MFFD- 1 A). Numerical tests are performed to illustrate the theoretical results and the superiority of SFFD preconditioner.

Original languageEnglish
Pages (from-to)1805-1818
Number of pages14
JournalApplied Mathematics and Computation
Issue number6
Publication statusPublished - 15 May 2010
Externally publishedYes


  • Fourier analysis
  • Frequency filtering decomposition
  • Linear system
  • Preconditioner

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