Iterative methods for ill-conditioned Toeplitz matrices

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

In this paper we study the use of the Sine Transform for preconditioning linear Toeplitz systems. We consider Toeplitz matrices with a real generating function that is nonnegative with only a small number of zeros. Then we can define a preconditioner of the form SnΛSn where Sn is the matrix describing the discrete Sine transform and Λ is a diagonal matrix. If we have full knowledge about f then we can show that the preconditioned system is of bounded condition number independly of n. We can obtain the same result for the case that we know only the position and order of the zeros of f. If we only know the matrix and its coefficients tj, we present Sine transform preconditioners that show in many examples the same numerical behaviour.

Original languageEnglish
Pages (from-to)177-190
Number of pages14
JournalCalcolo
Volume33
Issue number3
DOIs
StatePublished - 1996

Keywords

  • Conjugate gradient method
  • Sine Transform
  • Toeplitz matrix

Fingerprint

Dive into the research topics of 'Iterative methods for ill-conditioned Toeplitz matrices'. Together they form a unique fingerprint.

Cite this