Toeplitz preconditioners for toeplitz systems with nonnegative generating functions

Raymond H. CHAN*

*Corresponding author for this work

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

122 Citations (Scopus)

Abstract

The preconditioned conjugate gradient method is employed to solve Toeplitz systems Tnx = b where the generating functions of the n-by-n Toeplitz matrices Tn are continuous nonnegative periodic functions defined in [-π,π]. The preconditioned Cn are band Toeplitz matrices with band-widths independent of n. We prove that the spectra of Cn-1Tn are uniformly bounded by constants independent of n. In particular, we show that the solutions of Tnx = b can be obtained in O(nlogn) operations.

Original languageEnglish
Pages (from-to)333-345
Number of pages13
JournalIMA Journal of Numerical Analysis
Volume11
Issue number3
DOIs
Publication statusPublished - Jul 1991
Externally publishedYes

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