Approximate inverse-free preconditioners for Toeplitz matrices

You Wei Wen*, Wai Ki Ching, Kwok Po NG

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

4 Citations (Scopus)


In this paper, we propose approximate inverse-free preconditioners for solving Toeplitz systems. The preconditioners are constructed based on the famous Gohberg-Semencul formula. We show that if a Toeplitz matrix is generated by a positive bounded function and its entries enjoys the off-diagonal decay property, then the eigenvalues of the preconditioned matrix are clustered around one. Experimental results show that the proposed preconditioners are superior to other existing preconditioners in the literature.

Original languageEnglish
Pages (from-to)6856-6867
Number of pages12
JournalApplied Mathematics and Computation
Issue number16
Publication statusPublished - 15 Apr 2011

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Approximate inverse-free preconditioners
  • Gohberg-Semencul formula
  • Preconditioned conjugate gradient method
  • Toeplitz matrices


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