Circulant Preconditioners for Elliptic Problems

Hon Fu Raymond CHAN, Tony F. CHAN

Research output: Journal PublicationsJournal Article (refereed)peer-review


We propose and analyze the use of circulant preconditioners for the solution of elliptic problems via preconditioned iterative methods such as the conjugate gradient method Part of our motivation is to exploit the fast inversion of circulant systems via the Fast Fourier Transform FFT We prove that circulant preconditioners can be chosen so that the condition number of the preconditioned system can be reduced from O (n2) to O (n). Numerical experiments also indicatethat the preconditioned systems exhibit favorable clustering of eigen-values Both the computation based on averaging of the coecients of the elliptic operator and the inversion using FFTs of the circulant
preconditioners are highly parallelizable.
Original languageEnglish
Pages (from-to)77-101
Number of pages25
JournalNumerical Linear Algebra with Applications
Issue number1
Publication statusPublished - 1992
Externally publishedYes


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