Circulant preconditioners from B-splines

Raymond H. CHAN*, Tat-Ming TSO, Hai-Wei SUN

*Corresponding author for this work

Research output: Book Chapters | Papers in Conference ProceedingsConference paper (refereed)Researchpeer-review

5 Citations (Scopus)


In this paper, we propose a new family of circulant preconditioners for solving Toeplitz systems. They are based on B-splines. The R. Chan and T. Chan preconditioners can be constructed from the first and the second order B-splines. Numerical results show that preconditioners from higher-order B-splines perform much better than well-known ones even in the cases where the Toeplitz matrices are ill-conditioned. Like that of the other circulant preconditioners, the construction of B-spline preconditioners requires only the entries of the given Toeplitz matrix and does not require an apriori knowledge of its generating function. Thus they are most suitable for applications where the generating function of the given Toeplitz matrix is not known explicitly.

Original languageEnglish
Title of host publicationProceedings Volume 3162: Optical Science, Engineering and Instrumentation '97
EditorsFranklin T. LUK
Number of pages10
Publication statusPublished - 24 Oct 1997
Externally publishedYes
EventOptical Science, Engineering and Instrumentation '97 - San Diego, United States
Duration: 28 Jul 19971 Aug 1997

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


ConferenceOptical Science, Engineering and Instrumentation '97
Country/TerritoryUnited States
CitySan Diego


  • B-spline
  • Circulant matrix
  • Preconditioner
  • Toeplitz matrix


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