Circulant preconditioners for toeplitz matrices with positive continuous generating functions

Raymond H. CHAN*, Man Chung YEUNG

*Corresponding author for this work

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

31 Citations (Scopus)

Abstract

We consider the solution of n-by-n Toeplitz systems Anx = b by the preconditioned conjugate gradient method. The preconditioner Cn is the circulant matrix that minimizes ∥Bn − AnF over all circulant matrices Bn. We show that if the generating function f is a positive 2π-periodic continuous function, then the spectrum of the preconditioned system Cn−1 An will be clustered around one. In particular, if the preconditioned conjugate gradient method is applied to solve the preconditioned system, the convergence rate is superlinear.

Original languageEnglish
Pages (from-to)233-240
Number of pages8
JournalMathematics of Computation
Volume58
Issue number197
DOIs
Publication statusPublished - Jan 1992
Externally publishedYes

Fingerprint

Dive into the research topics of 'Circulant preconditioners for toeplitz matrices with positive continuous generating functions'. Together they form a unique fingerprint.

Cite this