Preconditioning random Toeplitz systems

Wen Fong Ke, King Fai Lai, Tsung Lin Lee, Ngai Ching Wong

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

It can be very slow in solving large Toeplitz system Tnx = b by the conjugate gradient method (CG), when the eigenvalues of Tn split apart. The preconditioning of a Toeplitz operator by the Strang circulants has been shown to be very efficient. In this paper, we study the applicability of the preconditioning method when a random noise exists. Together with rigorous discussions in theory, numerical examples are also given.

Original languageEnglish
Pages (from-to)757-770
Number of pages14
JournalJournal of Nonlinear and Convex Analysis
Volume17
Issue number4
Publication statusPublished - 2016 Jan 1

Fingerprint

Toeplitz System
Random Systems
Conjugate gradient method
Preconditioning
Random Noise
Toeplitz Operator
Conjugate Gradient Method
Strings
Eigenvalue
Numerical Examples

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology
  • Control and Optimization
  • Applied Mathematics

Cite this

Ke, W. F., Lai, K. F., Lee, T. L., & Wong, N. C. (2016). Preconditioning random Toeplitz systems. Journal of Nonlinear and Convex Analysis, 17(4), 757-770.
Ke, Wen Fong ; Lai, King Fai ; Lee, Tsung Lin ; Wong, Ngai Ching. / Preconditioning random Toeplitz systems. In: Journal of Nonlinear and Convex Analysis. 2016 ; Vol. 17, No. 4. pp. 757-770.
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Ke, WF, Lai, KF, Lee, TL & Wong, NC 2016, 'Preconditioning random Toeplitz systems', Journal of Nonlinear and Convex Analysis, vol. 17, no. 4, pp. 757-770.

Preconditioning random Toeplitz systems. / Ke, Wen Fong; Lai, King Fai; Lee, Tsung Lin; Wong, Ngai Ching.

In: Journal of Nonlinear and Convex Analysis, Vol. 17, No. 4, 01.01.2016, p. 757-770.

Research output: Contribution to journalArticle

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Ke WF, Lai KF, Lee TL, Wong NC. Preconditioning random Toeplitz systems. Journal of Nonlinear and Convex Analysis. 2016 Jan 1;17(4):757-770.